[{"language":[{"iso":"eng"}],"oa_version":"Preprint","article_number":"18","month":"01","publication":"Selecta Mathematica","main_file_link":[{"url":"https://arxiv.org/abs/2206.15240","open_access":"1"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issnl":["1022-1824"],"issn":["4321-1234"],"eissn":["1420-9020"]},"oa":1,"type":"journal_article","date_published":"2024-01-26T00:00:00Z","publisher":"Springer Nature","article_type":"original","quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","date_created":"2023-01-16T11:45:53Z","department":[{"_id":"TiBr"}],"publication_status":"epub_ahead","intvolume":" 30","OA_place":"repository","title":"On the local-global principle for isogenies of abelian surfaces","scopus_import":"1","_id":"12312","issue":"2","author":[{"last_name":"Lombardo","first_name":"Davide","full_name":"Lombardo, Davide"},{"id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","first_name":"Matteo","last_name":"Verzobio","orcid":"0000-0002-0854-0306","full_name":"Verzobio, Matteo"}],"OA_type":"green","volume":30,"acknowledgement":"It is a pleasure to thank Samuele Anni for his interest in this project and for several discussions on the topic of this paper, which led in particular to Remark 6.30 and to a better understanding of the difficulties with [6]. We also thank John Cullinan for correspondence about [6] and Barinder Banwait for his many insightful comments on the first version of this paper. Finally, we thank the referee for their thorough reading of the manuscript.\r\nOpen access funding provided by Università di Pisa within the CRUI-CARE Agreement. The authors have been partially supported by MIUR (Italy) through PRIN 2017 “Geometric, algebraic and analytic methods in arithmetic\" and PRIN 2022 “Semiabelian varieties, Galois representations and related Diophantine problems\", and by the University of Pisa through PRA 2018-19 and 2022 “Spazi di moduli, rappresentazioni e strutture combinatorie\". The first author is a member of the INdAM group GNSAGA.","day":"26","arxiv":1,"doi":"10.1007/s00029-023-00908-0","abstract":[{"text":"Let $\\ell$ be a prime number. We classify the subgroups $G$ of $\\operatorname{Sp}_4(\\mathbb{F}_\\ell)$ and $\\operatorname{GSp}_4(\\mathbb{F}_\\ell)$ that act irreducibly on $\\mathbb{F}_\\ell^4$, but such that every element of $G$ fixes an $\\mathbb{F}_\\ell$-vector subspace of dimension 1. We use this classification to prove that the local-global principle for isogenies of degree $\\ell$ between abelian surfaces over number fields holds in many cases -- in particular, whenever the abelian surface has non-trivial endomorphisms and $\\ell$ is large enough with respect to the field of definition. Finally, we prove that there exist arbitrarily large primes $\\ell$ for which some abelian surface\r\n$A/\\mathbb{Q}$ fails the local-global principle for isogenies of degree $\\ell$.","lang":"eng"}],"year":"2024","date_updated":"2025-02-13T11:47:12Z","external_id":{"arxiv":["2206.15240"]}},{"language":[{"iso":"eng"}],"month":"05","oa_version":"Preprint","publication":"Annals of Mathematics","related_material":{"link":[{"description":"News on IST Homepage","relation":"press_release","url":"https://ist.ac.at/en/news/when-is-necessary-sufficient/"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","main_file_link":[{"url":"https://arxiv.org/abs/2006.02356","open_access":"1"}],"oa":1,"publication_identifier":{"issn":["0003-486X"]},"oaworkID":1,"type":"journal_article","date_published":"2023-05-01T00:00:00Z","article_type":"original","publisher":"Princeton University","quality_controlled":"1","page":"1115-1203","intvolume":" 197","title":"The Hasse principle for random Fano hypersurfaces","department":[{"_id":"TiBr"}],"article_processing_charge":"No","date_created":"2020-10-19T14:28:50Z","publication_status":"published","issue":"3","author":[{"first_name":"Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Boudec, Pierre Le","last_name":"Boudec","first_name":"Pierre Le"},{"last_name":"Sawin","first_name":"Will","full_name":"Sawin, Will"}],"_id":"8682","volume":197,"abstract":[{"text":"It is known that the Brauer--Manin obstruction to the Hasse principle is vacuous for smooth Fano hypersurfaces of dimension at least 3 over any number field. Moreover, for such varieties it follows from a general conjecture of Colliot-Thélène that the Brauer--Manin obstruction to the Hasse principle should be the only one, so that the Hasse principle is expected to hold. Working over the field of rational numbers and ordering Fano hypersurfaces of fixed degree and dimension by height, we prove that almost every such hypersurface satisfies the Hasse principle provided that the dimension is at least 3. This proves a conjecture of Poonen and Voloch in every case except for cubic surfaces.","lang":"eng"}],"day":"01","arxiv":1,"doi":"10.4007/annals.2023.197.3.3","external_id":{"oaworkID":["w3033938593"],"arxiv":["2006.02356"],"isi":["000966611000003"]},"isi":1,"citation":{"short":"T.D. Browning, P.L. Boudec, W. Sawin, Annals of Mathematics 197 (2023) 1115–1203.","mla":"Browning, Timothy D., et al. “The Hasse Principle for Random Fano Hypersurfaces.” Annals of Mathematics, vol. 197, no. 3, Princeton University, 2023, pp. 1115–203, doi:10.4007/annals.2023.197.3.3.","ista":"Browning TD, Boudec PL, Sawin W. 2023. The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. 197(3), 1115–1203.","apa":"Browning, T. D., Boudec, P. L., & Sawin, W. (2023). The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. Princeton University. https://doi.org/10.4007/annals.2023.197.3.3","ama":"Browning TD, Boudec PL, Sawin W. The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. 2023;197(3):1115-1203. doi:10.4007/annals.2023.197.3.3","chicago":"Browning, Timothy D, Pierre Le Boudec, and Will Sawin. “The Hasse Principle for Random Fano Hypersurfaces.” Annals of Mathematics. Princeton University, 2023. https://doi.org/10.4007/annals.2023.197.3.3.","ieee":"T. D. Browning, P. L. Boudec, and W. Sawin, “The Hasse principle for random Fano hypersurfaces,” Annals of Mathematics, vol. 197, no. 3. Princeton University, pp. 1115–1203, 2023."},"year":"2023","date_updated":"2025-08-11T11:59:49Z"},{"year":"2023","citation":{"short":"T. Horesh, Y. Karasik, Quarterly Journal of Mathematics 74 (2023) 1253–1294.","mla":"Horesh, Tal, and Yakov Karasik. “Equidistribution of Primitive Lattices in ℝn.” Quarterly Journal of Mathematics, vol. 74, no. 4, Oxford University Press, 2023, pp. 1253–94, doi:10.1093/qmath/haad008.","ista":"Horesh T, Karasik Y. 2023. Equidistribution of primitive lattices in ℝn. Quarterly Journal of Mathematics. 74(4), 1253–1294.","ama":"Horesh T, Karasik Y. Equidistribution of primitive lattices in ℝn. Quarterly Journal of Mathematics. 2023;74(4):1253-1294. doi:10.1093/qmath/haad008","apa":"Horesh, T., & Karasik, Y. (2023). Equidistribution of primitive lattices in ℝn. Quarterly Journal of Mathematics. Oxford University Press. https://doi.org/10.1093/qmath/haad008","chicago":"Horesh, Tal, and Yakov Karasik. “Equidistribution of Primitive Lattices in ℝn.” Quarterly Journal of Mathematics. Oxford University Press, 2023. https://doi.org/10.1093/qmath/haad008.","ieee":"T. Horesh and Y. Karasik, “Equidistribution of primitive lattices in ℝn,” Quarterly Journal of Mathematics, vol. 74, no. 4. Oxford University Press, pp. 1253–1294, 2023."},"date_updated":"2024-01-02T07:39:55Z","external_id":{"arxiv":["2012.04508"]},"day":"01","arxiv":1,"doi":"10.1093/qmath/haad008","abstract":[{"text":"We count primitive lattices of rank d inside Zn as their covolume tends to infinity, with respect to certain parameters of such lattices. These parameters include, for example, the subspace that a lattice spans, namely its projection to the Grassmannian; its homothety class and its equivalence class modulo rescaling and rotation, often referred to as a shape. We add to a prior work of Schmidt by allowing sets in the spaces of parameters that are general enough to conclude the joint equidistribution of these parameters. In addition to the primitive d-lattices Λ themselves, we also consider their orthogonal complements in Zn, A1, and show that the equidistribution occurs jointly for Λ and A1. Finally, our asymptotic formulas for the number of primitive lattices include an explicit bound on the error term.","lang":"eng"}],"volume":74,"acknowledgement":"This work was done when both authors were visiting Institute of Science and Technology (IST) Austria. T.H. was being supported by Engineering and Physical Sciences Research Council grant EP/P026710/1. Y.K. had a great time there and is grateful for the hospitality. The appendix to this paper is largely based on a mini course T.H. had given at IST in February 2020.","ddc":["510"],"scopus_import":"1","_id":"14717","issue":"4","author":[{"last_name":"Horesh","first_name":"Tal","full_name":"Horesh, Tal","id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425"},{"first_name":"Yakov","last_name":"Karasik","full_name":"Karasik, Yakov"}],"department":[{"_id":"TiBr"}],"article_processing_charge":"Yes (via OA deal)","date_created":"2023-12-31T23:01:03Z","publication_status":"published","intvolume":" 74","title":"Equidistribution of primitive lattices in ℝn","quality_controlled":"1","page":"1253-1294","file_date_updated":"2024-01-02T07:37:09Z","publisher":"Oxford University Press","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2023-12-01T00:00:00Z","publication_identifier":{"issn":["0033-5606"],"eissn":["1464-3847"]},"oa":1,"file":[{"file_id":"14720","creator":"dernst","access_level":"open_access","success":1,"relation":"main_file","date_updated":"2024-01-02T07:37:09Z","content_type":"application/pdf","file_name":"2023_QuarterlyJourMath_Horesh.pdf","date_created":"2024-01-02T07:37:09Z","file_size":724748,"checksum":"bf29baa9eae8500f3374dbcb80712687"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","has_accepted_license":"1","publication":"Quarterly Journal of Mathematics","project":[{"grant_number":"EP-P026710-2","name":"Between rational and integral points","_id":"26A8D266-B435-11E9-9278-68D0E5697425"}],"oa_version":"Published Version","month":"12","language":[{"iso":"eng"}]},{"ddc":["510"],"acknowledgement":"The authors are grateful to Paul Nelson, Per Salberger and Jason Starr for useful comments. While working on this paper the first author was supported by EPRSC grant EP/P026710/1. The research was partially conducted during the period the second author served as a Clay Research Fellow, and partially conducted during the period he was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation.","volume":17,"external_id":{"isi":["000996014700004"],"arxiv":["1810.06882"]},"isi":1,"year":"2023","citation":{"ama":"Browning TD, Sawin W. Free rational curves on low degree hypersurfaces and the circle method. Algebra and Number Theory. 2023;17(3):719-748. doi:10.2140/ant.2023.17.719","apa":"Browning, T. D., & Sawin, W. (2023). Free rational curves on low degree hypersurfaces and the circle method. Algebra and Number Theory. Mathematical Sciences Publishers. https://doi.org/10.2140/ant.2023.17.719","chicago":"Browning, Timothy D, and Will Sawin. “Free Rational Curves on Low Degree Hypersurfaces and the Circle Method.” Algebra and Number Theory. 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Algebra and Number Theory. 17(3), 719–748."},"date_updated":"2023-08-01T14:51:57Z","abstract":[{"lang":"eng","text":"We use a function field version of the Hardy–Littlewood circle method to study the locus of free rational curves on an arbitrary smooth projective hypersurface of sufficiently low degree. On the one hand this allows us to bound the dimension of the singular locus of the moduli space of rational curves on such hypersurfaces and, on the other hand, it sheds light on Peyre’s reformulation of the Batyrev–Manin conjecture in terms of slopes with respect to the tangent bundle."}],"day":"12","arxiv":1,"doi":"10.2140/ant.2023.17.719","file_date_updated":"2023-05-30T08:05:22Z","quality_controlled":"1","page":"719-748","article_type":"original","publisher":"Mathematical Sciences Publishers","issue":"3","author":[{"full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Sawin, Will","last_name":"Sawin","first_name":"Will"}],"scopus_import":"1","_id":"13091","intvolume":" 17","title":"Free rational curves on low degree hypersurfaces and the circle method","date_created":"2023-05-28T22:01:02Z","department":[{"_id":"TiBr"}],"article_processing_charge":"No","publication_status":"published","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"success":1,"access_level":"open_access","relation":"main_file","creator":"dernst","file_id":"13101","checksum":"5d5d67b235905650e33cf7065d7583b4","file_size":1430719,"date_created":"2023-05-30T08:05:22Z","file_name":"2023_AlgebraNumberTheory_Browning.pdf","content_type":"application/pdf","date_updated":"2023-05-30T08:05:22Z"}],"type":"journal_article","date_published":"2023-04-12T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"eissn":["1944-7833"],"issn":["1937-0652"]},"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Algebra and Number Theory","month":"04","project":[{"grant_number":"EP-P026710-2","name":"Between rational and integral points","_id":"26A8D266-B435-11E9-9278-68D0E5697425"}],"oa_version":"Published Version"},{"publication":"Involve","month":"05","oa_version":"Preprint","language":[{"iso":"eng"}],"type":"journal_article","date_published":"2023-05-26T00:00:00Z","oa":1,"publication_identifier":{"eissn":["1944-4184"],"issn":["1944-4176"]},"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://arxiv.org/abs/2203.06881","open_access":"1"}],"issue":"2","author":[{"orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Lyczak, Julian","last_name":"Lyczak","first_name":"Julian","id":"3572849A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Sarapin","first_name":"Roman","full_name":"Sarapin, Roman"}],"scopus_import":"1","_id":"13180","intvolume":" 16","title":"Local solubility for a family of quadrics over a split quadric surface","department":[{"_id":"TiBr"}],"date_created":"2023-07-02T22:00:43Z","article_processing_charge":"No","publication_status":"published","quality_controlled":"1","page":"331-342","article_type":"original","publisher":"Mathematical Sciences Publishers","external_id":{"arxiv":["2203.06881"]},"citation":{"ieee":"T. D. Browning, J. Lyczak, and R. Sarapin, “Local solubility for a family of quadrics over a split quadric surface,” Involve, vol. 16, no. 2. Mathematical Sciences Publishers, pp. 331–342, 2023.","chicago":"Browning, Timothy D, Julian Lyczak, and Roman Sarapin. “Local Solubility for a Family of Quadrics over a Split Quadric Surface.” Involve. Mathematical Sciences Publishers, 2023. https://doi.org/10.2140/involve.2023.16.331.","ama":"Browning TD, Lyczak J, Sarapin R. Local solubility for a family of quadrics over a split quadric surface. Involve. 2023;16(2):331-342. doi:10.2140/involve.2023.16.331","apa":"Browning, T. D., Lyczak, J., & Sarapin, R. (2023). Local solubility for a family of quadrics over a split quadric surface. Involve. Mathematical Sciences Publishers. https://doi.org/10.2140/involve.2023.16.331","ista":"Browning TD, Lyczak J, Sarapin R. 2023. Local solubility for a family of quadrics over a split quadric surface. Involve. 16(2), 331–342.","mla":"Browning, Timothy D., et al. “Local Solubility for a Family of Quadrics over a Split Quadric Surface.” Involve, vol. 16, no. 2, Mathematical Sciences Publishers, 2023, pp. 331–42, doi:10.2140/involve.2023.16.331.","short":"T.D. Browning, J. Lyczak, R. Sarapin, Involve 16 (2023) 331–342."},"year":"2023","date_updated":"2023-07-17T08:39:19Z","abstract":[{"lang":"eng","text":"We study the density of everywhere locally soluble diagonal quadric surfaces, parameterised by rational points that lie on a split quadric surface"}],"day":"26","doi":"10.2140/involve.2023.16.331","arxiv":1,"volume":16},{"ddc":["510"],"acknowledgement":"This paper was completed as part of a project which received funding from the\r\nEuropean Union’s Horizon 2020 research and innovation programme under the Marie\r\nSkłodowska-Curie grant agreement No. 754411.","volume":73,"isi":1,"external_id":{"arxiv":["2005.14013"],"isi":["001000279500001"]},"date_updated":"2023-12-13T12:03:04Z","citation":{"chicago":"Lyczak, Julian. “Order 5 Brauer–Manin Obstructions to the Integral Hasse Principle on Log K3 Surfaces.” Annales de l’Institut Fourier. Association des Annales de l’Institut Fourier, 2023. https://doi.org/10.5802/aif.3529.","ieee":"J. Lyczak, “Order 5 Brauer–Manin obstructions to the integral Hasse principle on log K3 surfaces,” Annales de l’Institut Fourier, vol. 73, no. 2. Association des Annales de l’Institut Fourier, pp. 447–478, 2023.","ama":"Lyczak J. Order 5 Brauer–Manin obstructions to the integral Hasse principle on log K3 surfaces. Annales de l’Institut Fourier. 2023;73(2):447-478. doi:10.5802/aif.3529","apa":"Lyczak, J. (2023). Order 5 Brauer–Manin obstructions to the integral Hasse principle on log K3 surfaces. Annales de l’Institut Fourier. Association des Annales de l’Institut Fourier. https://doi.org/10.5802/aif.3529","ista":"Lyczak J. 2023. Order 5 Brauer–Manin obstructions to the integral Hasse principle on log K3 surfaces. Annales de l’Institut Fourier. 73(2), 447–478.","short":"J. Lyczak, Annales de l’Institut Fourier 73 (2023) 447–478.","mla":"Lyczak, Julian. “Order 5 Brauer–Manin Obstructions to the Integral Hasse Principle on Log K3 Surfaces.” Annales de l’Institut Fourier, vol. 73, no. 2, Association des Annales de l’Institut Fourier, 2023, pp. 447–78, doi:10.5802/aif.3529."},"year":"2023","abstract":[{"text":"We construct families of log K3 surfaces and study the arithmetic of their members. We use this to produce explicit surfaces with an order 5 Brauer–Manin obstruction to the integral Hasse principle.","lang":"eng"}],"arxiv":1,"doi":"10.5802/aif.3529","day":"12","file_date_updated":"2023-08-07T07:19:42Z","page":"447-478","ec_funded":1,"quality_controlled":"1","article_type":"original","publisher":"Association des Annales de l'Institut Fourier","author":[{"id":"3572849A-F248-11E8-B48F-1D18A9856A87","full_name":"Lyczak, Julian","last_name":"Lyczak","first_name":"Julian"}],"issue":"2","_id":"13973","license":"https://creativecommons.org/licenses/by-nd/4.0/","scopus_import":"1","title":"Order 5 Brauer–Manin obstructions to the integral Hasse principle on log K3 surfaces","intvolume":" 73","publication_status":"published","department":[{"_id":"TiBr"}],"article_processing_charge":"Yes (in subscription journal)","date_created":"2023-08-06T22:01:12Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"date_created":"2023-08-07T07:19:42Z","checksum":"daf53fc614c894422e4c0fb3d2a2ae3e","file_size":1529821,"date_updated":"2023-08-07T07:19:42Z","file_name":"2023_AnnalesFourier_Lyczak.pdf","content_type":"application/pdf","relation":"main_file","success":1,"access_level":"open_access","file_id":"13977","creator":"dernst"}],"date_published":"2023-05-12T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)"},"oa":1,"publication_identifier":{"issn":["0373-0956"]},"language":[{"iso":"eng"}],"publication":"Annales de l'Institut Fourier","has_accepted_license":"1","month":"05","oa_version":"Published Version","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}]},{"has_accepted_license":"1","publication":"Pacific Journal of Mathematics","oa_version":"Published Version","month":"07","language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2023-07-26T00:00:00Z","publication_identifier":{"issn":["0030-8730"],"eissn":["1945-5844"]},"oa":1,"file":[{"date_created":"2023-09-05T07:26:17Z","checksum":"a675b53cfb31fa46be1e879b7e77fe8c","file_size":654895,"date_updated":"2023-09-05T07:26:17Z","content_type":"application/pdf","file_name":"2023_PacificJourMaths_Horesh.pdf","success":1,"access_level":"open_access","relation":"main_file","file_id":"14267","creator":"dernst"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","_id":"14245","issue":"2","author":[{"id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425","first_name":"Tal","last_name":"Horesh","full_name":"Horesh, Tal"},{"full_name":"Nevo, Amos","first_name":"Amos","last_name":"Nevo"}],"department":[{"_id":"TiBr"}],"date_created":"2023-08-27T22:01:18Z","article_processing_charge":"Yes","publication_status":"published","intvolume":" 324","title":"Horospherical coordinates of lattice points in hyperbolic spaces: Effective counting and equidistribution","quality_controlled":"1","page":"265-294","file_date_updated":"2023-09-05T07:26:17Z","publisher":"Mathematical Sciences Publishers","article_type":"original","citation":{"short":"T. Horesh, A. Nevo, Pacific Journal of Mathematics 324 (2023) 265–294.","mla":"Horesh, Tal, and Amos Nevo. “Horospherical Coordinates of Lattice Points in Hyperbolic Spaces: Effective Counting and Equidistribution.” Pacific Journal of Mathematics, vol. 324, no. 2, Mathematical Sciences Publishers, 2023, pp. 265–94, doi:10.2140/pjm.2023.324.265.","ista":"Horesh T, Nevo A. 2023. Horospherical coordinates of lattice points in hyperbolic spaces: Effective counting and equidistribution. Pacific Journal of Mathematics. 324(2), 265–294.","apa":"Horesh, T., & Nevo, A. (2023). Horospherical coordinates of lattice points in hyperbolic spaces: Effective counting and equidistribution. Pacific Journal of Mathematics. Mathematical Sciences Publishers. https://doi.org/10.2140/pjm.2023.324.265","ama":"Horesh T, Nevo A. Horospherical coordinates of lattice points in hyperbolic spaces: Effective counting and equidistribution. Pacific Journal of Mathematics. 2023;324(2):265-294. doi:10.2140/pjm.2023.324.265","ieee":"T. Horesh and A. Nevo, “Horospherical coordinates of lattice points in hyperbolic spaces: Effective counting and equidistribution,” Pacific Journal of Mathematics, vol. 324, no. 2. Mathematical Sciences Publishers, pp. 265–294, 2023.","chicago":"Horesh, Tal, and Amos Nevo. “Horospherical Coordinates of Lattice Points in Hyperbolic Spaces: Effective Counting and Equidistribution.” Pacific Journal of Mathematics. Mathematical Sciences Publishers, 2023. https://doi.org/10.2140/pjm.2023.324.265."},"year":"2023","date_updated":"2023-12-13T12:19:42Z","external_id":{"isi":["001047690500001"],"arxiv":["1612.08215"]},"isi":1,"day":"26","arxiv":1,"doi":"10.2140/pjm.2023.324.265","abstract":[{"lang":"eng","text":"We establish effective counting results for lattice points in families of domains in real, complex and quaternionic hyperbolic spaces of any dimension. The domains we focus on are defined as product sets with respect to an Iwasawa decomposition. Several natural diophantine problems can be reduced to counting lattice points in such domains. These include equidistribution of the ratio of the length of the shortest solution (x,y) to the gcd equation bx−ay=1 relative to the length of (a,b), where (a,b) ranges over primitive vectors in a disc whose radius increases, the natural analog of this problem in imaginary quadratic number fields, as well as equidistribution of integral solutions to the diophantine equation defined by an integral Lorentz form in three or more variables. We establish an effective rate of convergence for these equidistribution problems, depending on the size of the spectral gap associated with a suitable lattice subgroup in the isometry group of the relevant hyperbolic space. The main result underlying our discussion amounts to establishing effective joint equidistribution for the horospherical component and the radial component in the Iwasawa decomposition of lattice elements."}],"acknowledgement":"The authors thank the referee for important comments which led to significant improvements is the presentation of several results in the paper. They also thank Ami Paz for preparing the figures for this paper. Horesh thanks Ami Paz and Yakov Karasik for helpful discussions. Nevo thanks John Parker and Rene Rühr for providing some very useful references. Nevo is supported by ISF Grant No. 2095/15.","volume":324,"ddc":["510"]},{"date_published":"2023-04-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1901.08503"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","publication":"International Mathematics Research Notices","oa_version":"Preprint","month":"04","language":[{"iso":"eng"}],"date_updated":"2023-08-01T12:23:55Z","citation":{"chicago":"Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Log Fano Threefold.” International Mathematics Research Notices. Oxford Academic, 2023. https://doi.org/10.1093/imrn/rnac048.","ieee":"F. A. Wilsch, “Integral points of bounded height on a log Fano threefold,” International Mathematics Research Notices, vol. 2023, no. 8. Oxford Academic, pp. 6780–6808, 2023.","ama":"Wilsch FA. Integral points of bounded height on a log Fano threefold. International Mathematics Research Notices. 2023;2023(8):6780-6808. doi:10.1093/imrn/rnac048","apa":"Wilsch, F. A. (2023). Integral points of bounded height on a log Fano threefold. International Mathematics Research Notices. Oxford Academic. https://doi.org/10.1093/imrn/rnac048","ista":"Wilsch FA. 2023. Integral points of bounded height on a log Fano threefold. International Mathematics Research Notices. 2023(8), 6780–6808.","short":"F.A. Wilsch, International Mathematics Research Notices 2023 (2023) 6780–6808.","mla":"Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Log Fano Threefold.” International Mathematics Research Notices, vol. 2023, no. 8, Oxford Academic, 2023, pp. 6780–808, doi:10.1093/imrn/rnac048."},"year":"2023","isi":1,"external_id":{"arxiv":["1901.08503"],"isi":["000773116000001"]},"arxiv":1,"doi":"10.1093/imrn/rnac048","day":"01","abstract":[{"text":"We determine an asymptotic formula for the number of integral points of bounded height on a blow-up of P3 outside certain planes using universal torsors.","lang":"eng"}],"volume":2023,"acknowledgement":"This work was supported by the German Academic Exchange Service. Parts of this article were prepared at the Institut de Mathémathiques de Jussieu—Paris Rive Gauche. I wish to thank Antoine Chambert-Loir for his remarks and the institute for its hospitality, as well as the anonymous referee for several useful remarks and suggestions for improvements.","_id":"9034","author":[{"first_name":"Florian Alexander","last_name":"Wilsch","orcid":"0000-0001-7302-8256","full_name":"Wilsch, Florian Alexander","id":"560601DA-8D36-11E9-A136-7AC1E5697425"}],"issue":"8","publication_status":"published","article_processing_charge":"No","date_created":"2021-01-22T09:31:09Z","department":[{"_id":"TiBr"}],"title":"Integral points of bounded height on a log Fano threefold","intvolume":" 2023","page":"6780-6808","quality_controlled":"1","publisher":"Oxford Academic","article_type":"original"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"date_created":"2023-11-13T09:50:41Z","file_size":389897,"checksum":"b6218d16a72742d8bb38d6fc3c9bb8c6","date_updated":"2023-11-13T09:50:41Z","content_type":"application/pdf","file_name":"2023_PacificJourMaths_Verzobio.pdf","access_level":"open_access","relation":"main_file","success":1,"file_id":"14525","creator":"dernst"}],"date_published":"2023-11-03T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"eissn":["0030-8730"]},"language":[{"iso":"eng"}],"publication":"Pacific Journal of Mathematics","has_accepted_license":"1","month":"11","oa_version":"Published Version","project":[{"grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"ddc":["510"],"acknowledgement":"This paper is part of the author’s PhD thesis at Università of Pisa. Moreover, this\r\nproject has received funding from the European Union’s Horizon 2020 research\r\nand innovation programme under the Marie Skłodowska-Curie Grant Agreement\r\nNo. 101034413. I thank the referee for many helpful comments.","volume":325,"isi":1,"external_id":{"arxiv":["2001.02987"],"isi":["001104766900001"]},"date_updated":"2023-12-13T11:18:14Z","citation":{"mla":"Verzobio, Matteo. “Some Effectivity Results for Primitive Divisors of Elliptic Divisibility Sequences.” Pacific Journal of Mathematics, vol. 325, no. 2, Mathematical Sciences Publishers, 2023, pp. 331–51, doi:10.2140/pjm.2023.325.331.","short":"M. Verzobio, Pacific Journal of Mathematics 325 (2023) 331–351.","ista":"Verzobio M. 2023. Some effectivity results for primitive divisors of elliptic divisibility sequences. Pacific Journal of Mathematics. 325(2), 331–351.","apa":"Verzobio, M. (2023). Some effectivity results for primitive divisors of elliptic divisibility sequences. Pacific Journal of Mathematics. Mathematical Sciences Publishers. https://doi.org/10.2140/pjm.2023.325.331","ama":"Verzobio M. Some effectivity results for primitive divisors of elliptic divisibility sequences. Pacific Journal of Mathematics. 2023;325(2):331-351. doi:10.2140/pjm.2023.325.331","chicago":"Verzobio, Matteo. “Some Effectivity Results for Primitive Divisors of Elliptic Divisibility Sequences.” Pacific Journal of Mathematics. Mathematical Sciences Publishers, 2023. https://doi.org/10.2140/pjm.2023.325.331.","ieee":"M. Verzobio, “Some effectivity results for primitive divisors of elliptic divisibility sequences,” Pacific Journal of Mathematics, vol. 325, no. 2. Mathematical Sciences Publishers, pp. 331–351, 2023."},"year":"2023","abstract":[{"text":"Let P be a nontorsion point on an elliptic curve defined over a number field K and consider the sequence {Bn}n∈N of the denominators of x(nP). We prove that every term of the sequence of the Bn has a primitive divisor for n greater than an effectively computable constant that we will explicitly compute. This constant will depend only on the model defining the curve.","lang":"eng"}],"doi":"10.2140/pjm.2023.325.331","arxiv":1,"day":"03","file_date_updated":"2023-11-13T09:50:41Z","page":"331-351","ec_funded":1,"quality_controlled":"1","article_type":"original","publisher":"Mathematical Sciences Publishers","author":[{"id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","full_name":"Verzobio, Matteo","orcid":"0000-0002-0854-0306","last_name":"Verzobio","first_name":"Matteo"}],"issue":"2","_id":"12313","scopus_import":"1","title":"Some effectivity results for primitive divisors of elliptic divisibility sequences","intvolume":" 325","publication_status":"published","date_created":"2023-01-16T11:46:19Z","department":[{"_id":"TiBr"}],"article_processing_charge":"Yes (in subscription journal)"},{"oa_version":"Preprint","month":"01","publication":"Proceedings of the American Mathematical Society","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0002-9939"],"eissn":["1088-6826"]},"oa":1,"type":"journal_article","date_published":"2023-01-01T00:00:00Z","main_file_link":[{"url":"https://hal.science/hal-03013498/","open_access":"1"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","date_created":"2023-01-29T23:00:58Z","department":[{"_id":"TiBr"}],"article_processing_charge":"No","publication_status":"published","intvolume":" 151","title":"Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups","scopus_import":"1","_id":"12427","issue":"3","author":[{"full_name":"Balestrieri, Francesca","last_name":"Balestrieri","first_name":"Francesca","id":"3ACCD756-F248-11E8-B48F-1D18A9856A87"}],"publisher":"American Mathematical Society","article_type":"original","quality_controlled":"1","page":"907-914","day":"01","doi":"10.1090/proc/15239","abstract":[{"text":"Let k be a number field and X a smooth, geometrically integral quasi-projective variety over k. For any linear algebraic group G over k and any G-torsor g : Z → X, we observe that if the étale-Brauer obstruction is the only one for strong approximation off a finite set of places S for all twists of Z by elements in H^1(k, G), then the étale-Brauer obstruction is the only one for strong approximation off a finite set of places S for X. As an application, we show that any homogeneous space of the form G/H with G a connected linear algebraic group over k satisfies strong approximation off the infinite places with étale-Brauer obstruction, under some compactness assumptions when k is totally real. We also prove more refined strong approximation results for homogeneous spaces of the form G/H with G semisimple simply connected and H finite, using the theory of torsors and descent.","lang":"eng"}],"year":"2023","citation":{"ista":"Balestrieri F. 2023. Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups. Proceedings of the American Mathematical Society. 151(3), 907–914.","mla":"Balestrieri, Francesca. “Some Remarks on Strong Approximation and Applications to Homogeneous Spaces of Linear Algebraic Groups.” Proceedings of the American Mathematical Society, vol. 151, no. 3, American Mathematical Society, 2023, pp. 907–14, doi:10.1090/proc/15239.","short":"F. Balestrieri, Proceedings of the American Mathematical Society 151 (2023) 907–914.","chicago":"Balestrieri, Francesca. “Some Remarks on Strong Approximation and Applications to Homogeneous Spaces of Linear Algebraic Groups.” Proceedings of the American Mathematical Society. American Mathematical Society, 2023. https://doi.org/10.1090/proc/15239.","ieee":"F. Balestrieri, “Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups,” Proceedings of the American Mathematical Society, vol. 151, no. 3. American Mathematical Society, pp. 907–914, 2023.","apa":"Balestrieri, F. (2023). Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/15239","ama":"Balestrieri F. Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups. Proceedings of the American Mathematical Society. 2023;151(3):907-914. doi:10.1090/proc/15239"},"date_updated":"2023-08-01T13:03:32Z","external_id":{"isi":["000898440000001"]},"isi":1,"volume":151},{"language":[{"iso":"eng"}],"oa_version":"Preprint","month":"02","publication":"Annali della Scuola Normale Superiore di Pisa - Classe di Scienze","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2007.14182","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","publication_identifier":{"eissn":["2036-2145"],"issn":["0391-173X"]},"oa":1,"date_published":"2023-02-16T00:00:00Z","type":"journal_article","publisher":"Scuola Normale Superiore - Edizioni della Normale","article_type":"original","page":"173-204","quality_controlled":"1","publication_status":"published","department":[{"_id":"TiBr"}],"date_created":"2023-05-07T22:01:04Z","article_processing_charge":"No","title":"Uniform bounds for rational points on hyperelliptic fibrations","intvolume":" 24","_id":"12916","scopus_import":"1","author":[{"full_name":"Bonolis, Dante","first_name":"Dante","last_name":"Bonolis","id":"6A459894-5FDD-11E9-AF35-BB24E6697425"},{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","first_name":"Timothy D","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177"}],"issue":"1","volume":24,"doi":"10.2422/2036-2145.202010_018","arxiv":1,"day":"16","abstract":[{"lang":"eng","text":"We apply a variant of the square-sieve to produce an upper bound for the number of rational points of bounded height on a family of surfaces that admit a fibration over P1 whose general fibre is a hyperelliptic curve. The implied constant does not depend on the coefficients of the polynomial defining the surface.\r\n"}],"date_updated":"2023-10-18T06:54:30Z","citation":{"chicago":"Bonolis, Dante, and Timothy D Browning. “Uniform Bounds for Rational Points on Hyperelliptic Fibrations.” Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze. Scuola Normale Superiore - Edizioni della Normale, 2023. https://doi.org/10.2422/2036-2145.202010_018.","ieee":"D. Bonolis and T. D. Browning, “Uniform bounds for rational points on hyperelliptic fibrations,” Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, vol. 24, no. 1. Scuola Normale Superiore - Edizioni della Normale, pp. 173–204, 2023.","apa":"Bonolis, D., & Browning, T. D. (2023). Uniform bounds for rational points on hyperelliptic fibrations. Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze. Scuola Normale Superiore - Edizioni della Normale. https://doi.org/10.2422/2036-2145.202010_018","ama":"Bonolis D, Browning TD. Uniform bounds for rational points on hyperelliptic fibrations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 2023;24(1):173-204. doi:10.2422/2036-2145.202010_018","ista":"Bonolis D, Browning TD. 2023. Uniform bounds for rational points on hyperelliptic fibrations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 24(1), 173–204.","short":"D. Bonolis, T.D. Browning, Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze 24 (2023) 173–204.","mla":"Bonolis, Dante, and Timothy D. Browning. “Uniform Bounds for Rational Points on Hyperelliptic Fibrations.” Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze, vol. 24, no. 1, Scuola Normale Superiore - Edizioni della Normale, 2023, pp. 173–204, doi:10.2422/2036-2145.202010_018."},"year":"2023","external_id":{"arxiv":["2007.14182"]}},{"acknowledgement":"We are grateful to Mikhail Borovoi, Zeev Rudnick and Olivier Wienberg for their interest in our\r\nwork. We would like to address our gratitude to Ulrich Derenthal for his generous support at Leibniz Universitat Hannover. We are in debt to Tim Browning for an enlightening discussion and to the anonymous referees for critical comments, which lead to overall improvements of various preliminary versions of this paper. Part of this work was carried out and reported during a visit to the University of Science and Technology of China. We thank Yongqi Liang for offering warm hospitality. The first author was supported by a Humboldt-Forschungsstipendium. The second author was supported by grant DE 1646/4-2 of the Deutsche Forschungsgemeinschaft.","volume":398,"abstract":[{"lang":"eng","text":"We establish the Hardy-Littlewood property (à la Borovoi-Rudnick) for Zariski open subsets in affine quadrics of the form q(x1,...,xn)=m, where q is a non-degenerate integral quadratic form in n>3 variables and m is a non-zero integer. This gives asymptotic formulas for the density of integral points taking coprime polynomial values, which is a quantitative version of the arithmetic purity of strong approximation property off infinity for affine quadrics."}],"arxiv":1,"doi":"10.1016/j.aim.2022.108236","day":"26","isi":1,"external_id":{"arxiv":["2003.07287"],"isi":["000792517300014"]},"date_updated":"2023-08-02T14:24:18Z","year":"2022","citation":{"mla":"Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood Property and Geometric Sieve for Affine Quadrics.” Advances in Mathematics, vol. 398, no. 3, 108236, Elsevier, 2022, doi:10.1016/j.aim.2022.108236.","short":"Y. Cao, Z. Huang, Advances in Mathematics 398 (2022).","ista":"Cao Y, Huang Z. 2022. Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. Advances in Mathematics. 398(3), 108236.","apa":"Cao, Y., & Huang, Z. (2022). Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2022.108236","ama":"Cao Y, Huang Z. Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. Advances in Mathematics. 2022;398(3). doi:10.1016/j.aim.2022.108236","ieee":"Y. Cao and Z. Huang, “Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics,” Advances in Mathematics, vol. 398, no. 3. Elsevier, 2022.","chicago":"Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood Property and Geometric Sieve for Affine Quadrics.” Advances in Mathematics. Elsevier, 2022. https://doi.org/10.1016/j.aim.2022.108236."},"article_type":"original","publisher":"Elsevier","quality_controlled":"1","title":"Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics","intvolume":" 398","publication_status":"published","date_created":"2022-02-20T23:01:30Z","department":[{"_id":"TiBr"}],"article_processing_charge":"No","author":[{"full_name":"Cao, Yang","first_name":"Yang","last_name":"Cao"},{"id":"21f1b52f-2fd1-11eb-a347-a4cdb9b18a51","full_name":"Huang, Zhizhong","first_name":"Zhizhong","last_name":"Huang"}],"issue":"3","_id":"10765","scopus_import":"1","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2003.07287"}],"oa":1,"publication_identifier":{"eissn":["1090-2082"],"issn":["0001-8708"]},"date_published":"2022-03-26T00:00:00Z","type":"journal_article","language":[{"iso":"eng"}],"month":"03","article_number":"108236","oa_version":"Preprint","publication":"Advances in Mathematics"},{"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"Part of this work was conducted as a guest at the Institut de Mathématiques de Jussieu–Paris Rive Gauche invited by Antoine Chambert-Loir and funded by DAAD.\r\nDuring this time, I had interesting and fruitful discussions on the interpretation of the result for\r\nthe toric variety discussed in Section 3 with Antoine Chambert-Loir. I wish to thank him for these\r\nopportunities and for his useful remarks on earlier versions of this article. This work was partly\r\nfunded by FWF grant P 32428-N35.","main_file_link":[{"url":"https://arxiv.org/abs/2202.10909","open_access":"1"}],"date_published":"2022-02-22T00:00:00Z","type":"preprint","external_id":{"arxiv":["2202.10909"]},"date_updated":"2023-05-03T07:46:35Z","year":"2022","citation":{"ista":"Wilsch FA. Integral points of bounded height on a certain toric variety. arXiv, 2202.10909.","mla":"Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Certain Toric Variety.” ArXiv, 2202.10909, doi:10.48550/arXiv.2202.10909.","short":"F.A. Wilsch, ArXiv (n.d.).","chicago":"Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Certain Toric Variety.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2202.10909.","ieee":"F. A. Wilsch, “Integral points of bounded height on a certain toric variety,” arXiv. .","apa":"Wilsch, F. A. (n.d.). Integral points of bounded height on a certain toric variety. arXiv. https://doi.org/10.48550/arXiv.2202.10909","ama":"Wilsch FA. Integral points of bounded height on a certain toric variety. arXiv. doi:10.48550/arXiv.2202.10909"},"abstract":[{"text":"We determine an asymptotic formula for the number of integral points of\r\nbounded height on a certain toric variety, which is incompatible with part of a\r\npreprint by Chambert-Loir and Tschinkel. We provide an alternative\r\ninterpretation of the asymptotic formula we get. To do so, we construct an\r\nanalogue of Peyre's constant $\\alpha$ and describe its relation to a new\r\nobstruction to the Zariski density of integral points in certain regions of\r\nvarieties.","lang":"eng"}],"oa":1,"doi":"10.48550/arXiv.2202.10909","arxiv":1,"day":"22","language":[{"iso":"eng"}],"keyword":["Integral point","toric variety","Manin's conjecture"],"author":[{"id":"560601DA-8D36-11E9-A136-7AC1E5697425","first_name":"Florian Alexander","last_name":"Wilsch","orcid":"0000-0001-7302-8256","full_name":"Wilsch, Florian Alexander"}],"_id":"10788","publication":"arXiv","month":"02","title":"Integral points of bounded height on a certain toric variety","article_number":"2202.10909","publication_status":"submitted","oa_version":"Preprint","project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"P32428","name":"New frontiers of the Manin conjecture"}],"date_created":"2022-02-23T09:04:43Z","article_processing_charge":"No","department":[{"_id":"TiBr"}]},{"month":"10","article_number":"102085","oa_version":"Published Version","publication":"Finite Fields and their Applications","has_accepted_license":"1","language":[{"iso":"eng"}],"oa":1,"publication_identifier":{"issn":["10715797"],"eissn":["10902465"]},"date_published":"2022-10-01T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"file_size":247615,"checksum":"3ca88decb1011180dc6de7e0862153e1","date_created":"2023-02-02T07:56:34Z","file_name":"2022_FiniteFields_Kmentt.pdf","content_type":"application/pdf","date_updated":"2023-02-02T07:56:34Z","success":1,"relation":"main_file","access_level":"open_access","creator":"dernst","file_id":"12475"}],"title":"The Bertini irreducibility theorem for higher codimensional slices","intvolume":" 83","publication_status":"published","department":[{"_id":"TiBr"}],"date_created":"2022-07-24T22:01:41Z","article_processing_charge":"Yes (via OA deal)","author":[{"id":"c90670c9-0bf0-11ed-86f5-ed522ece2fac","full_name":"Kmentt, Philip","last_name":"Kmentt","first_name":"Philip"},{"id":"440EB050-F248-11E8-B48F-1D18A9856A87","full_name":"Shute, Alec L","orcid":"0000-0002-1812-2810","last_name":"Shute","first_name":"Alec L"}],"issue":"10","_id":"11636","scopus_import":"1","article_type":"original","publisher":"Elsevier","file_date_updated":"2023-02-02T07:56:34Z","quality_controlled":"1","abstract":[{"text":"In [3], Poonen and Slavov recently developed a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing. In this paper, we extend their work by proving an analogous bound for the dimension of the exceptional locus in the setting of linear subspaces of higher codimensions.","lang":"eng"}],"doi":"10.1016/j.ffa.2022.102085","arxiv":1,"day":"01","isi":1,"external_id":{"isi":["000835490600001"],"arxiv":["2111.06697"]},"date_updated":"2023-08-03T12:12:57Z","year":"2022","citation":{"apa":"Kmentt, P., & Shute, A. L. (2022). The Bertini irreducibility theorem for higher codimensional slices. Finite Fields and Their Applications. Elsevier. https://doi.org/10.1016/j.ffa.2022.102085","ama":"Kmentt P, Shute AL. The Bertini irreducibility theorem for higher codimensional slices. Finite Fields and their Applications. 2022;83(10). doi:10.1016/j.ffa.2022.102085","chicago":"Kmentt, Philip, and Alec L Shute. “The Bertini Irreducibility Theorem for Higher Codimensional Slices.” Finite Fields and Their Applications. Elsevier, 2022. https://doi.org/10.1016/j.ffa.2022.102085.","ieee":"P. Kmentt and A. L. Shute, “The Bertini irreducibility theorem for higher codimensional slices,” Finite Fields and their Applications, vol. 83, no. 10. Elsevier, 2022.","mla":"Kmentt, Philip, and Alec L. Shute. “The Bertini Irreducibility Theorem for Higher Codimensional Slices.” Finite Fields and Their Applications, vol. 83, no. 10, 102085, Elsevier, 2022, doi:10.1016/j.ffa.2022.102085.","short":"P. Kmentt, A.L. Shute, Finite Fields and Their Applications 83 (2022).","ista":"Kmentt P, Shute AL. 2022. The Bertini irreducibility theorem for higher codimensional slices. Finite Fields and their Applications. 83(10), 102085."},"ddc":["510"],"volume":83},{"quality_controlled":"1","page":"2385-2407","article_type":"original","publisher":"Mathematical Sciences Publishers","issue":"10","author":[{"first_name":"Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Horesh, Tal","last_name":"Horesh","first_name":"Tal","id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425"},{"id":"560601DA-8D36-11E9-A136-7AC1E5697425","last_name":"Wilsch","first_name":"Florian Alexander","full_name":"Wilsch, Florian Alexander","orcid":"0000-0001-7302-8256"}],"scopus_import":"1","_id":"9199","intvolume":" 16","title":"Equidistribution and freeness on Grassmannians","department":[{"_id":"TiBr"}],"date_created":"2021-02-25T09:56:57Z","article_processing_charge":"No","publication_status":"published","volume":16,"acknowledgement":"The authors are very grateful to Will Sawin for useful remarks about this topic. While working on this paper the first two authors were supported by EPSRC grant EP/P026710/1, and the first and last authors by FWF grant P 32428-N35.","external_id":{"isi":["000961514100004"],"arxiv":["2102.11552"]},"isi":1,"citation":{"mla":"Browning, Timothy D., et al. “Equidistribution and Freeness on Grassmannians.” Algebra & Number Theory, vol. 16, no. 10, Mathematical Sciences Publishers, 2022, pp. 2385–407, doi:10.2140/ant.2022.16.2385.","short":"T.D. Browning, T. Horesh, F.A. Wilsch, Algebra & Number Theory 16 (2022) 2385–2407.","ista":"Browning TD, Horesh T, Wilsch FA. 2022. Equidistribution and freeness on Grassmannians. Algebra & Number Theory. 16(10), 2385–2407.","apa":"Browning, T. D., Horesh, T., & Wilsch, F. A. (2022). Equidistribution and freeness on Grassmannians. Algebra & Number Theory. Mathematical Sciences Publishers. https://doi.org/10.2140/ant.2022.16.2385","ama":"Browning TD, Horesh T, Wilsch FA. Equidistribution and freeness on Grassmannians. 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These lattices are related to the tangent bundle of Grassmannians and their study is motivated by Peyre's programme on \"freeness\" for rational points of bounded height on Fano\r\nvarieties."}],"day":"01","doi":"10.2140/ant.2022.16.2385","arxiv":1,"language":[{"iso":"eng"}],"publication":"Algebra & Number Theory","month":"12","project":[{"grant_number":"EP-P026710-2","name":"Between rational and integral points","_id":"26A8D266-B435-11E9-9278-68D0E5697425"},{"grant_number":"P32428","name":"New frontiers of the Manin conjecture","call_identifier":"FWF","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425"}],"oa_version":"Preprint","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"url":"https://arxiv.org/abs/2102.11552","open_access":"1"}],"type":"journal_article","date_published":"2022-12-01T00:00:00Z","oa":1,"publication_identifier":{"eissn":["1944-7833"],"issn":["1937-0652"]}},{"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Mathematical Proceedings of the Cambridge Philosophical Society","oa_version":"Published Version","month":"05","file":[{"creator":"cchlebak","file_id":"10395","relation":"main_file","success":1,"access_level":"open_access","content_type":"application/pdf","file_name":"2021_MathProcCamPhilSoc_Bonolis.pdf","date_updated":"2021-12-01T14:01:54Z","checksum":"614d2e9b83a78100408e4ee7752a80a8","file_size":334064,"date_created":"2021-12-01T14:01:54Z"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2022-05-01T00:00:00Z","publication_identifier":{"issn":["0305-0041"],"eissn":["1469-8064"]},"oa":1,"quality_controlled":"1","page":"563 - 590","file_date_updated":"2021-12-01T14:01:54Z","publisher":"Cambridge University Press","article_type":"original","scopus_import":"1","_id":"9364","issue":"3","author":[{"full_name":"Bonolis, Dante","last_name":"Bonolis","first_name":"Dante","id":"6A459894-5FDD-11E9-AF35-BB24E6697425"}],"date_created":"2021-05-02T22:01:29Z","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"TiBr"}],"publication_status":"published","intvolume":" 172","title":"On the size of the maximum of incomplete Kloosterman sums","volume":172,"acknowledgement":"I am most thankful to my advisor, Emmanuel Kowalski, for suggesting this problem and for his guidance during these years. I also would like to thank Youness Lamzouri for informing me about his work on sum of incomplete Birch sums and Tal Horesh for her suggestions on a previous version of the paper. Finally, I am very grateful to the anonymous referee for their careful reading of the manuscript and their valuable comments.","ddc":["510"],"year":"2022","citation":{"short":"D. Bonolis, Mathematical Proceedings of the Cambridge Philosophical Society 172 (2022) 563–590.","mla":"Bonolis, Dante. “On the Size of the Maximum of Incomplete Kloosterman Sums.” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 172, no. 3, Cambridge University Press, 2022, pp. 563–90, doi:10.1017/S030500412100030X.","ista":"Bonolis D. 2022. On the size of the maximum of incomplete Kloosterman sums. Mathematical Proceedings of the Cambridge Philosophical Society. 172(3), 563–590.","apa":"Bonolis, D. (2022). On the size of the maximum of incomplete Kloosterman sums. 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Cambridge University Press, pp. 563–590, 2022."},"date_updated":"2023-08-02T06:47:48Z","external_id":{"isi":["000784421500001"],"arxiv":["1811.10563"]},"isi":1,"day":"01","arxiv":1,"doi":"10.1017/S030500412100030X","abstract":[{"lang":"eng","text":"Let t : Fp → C be a complex valued function on Fp. A classical problem in analytic number theory is bounding the maximum M(t) := max 0≤H 0 there exists a large subset of a ∈ F×p such that for kl a,1,p : x → e((ax+x) / p) we have M(kla,1,p) ≥ (1−ε/√2π + o(1)) log log p, as p→∞. Finally, we prove a result on the growth of the moments of {M (kla,1,p)}a∈F×p. 2020 Mathematics Subject Classification: 11L03, 11T23 (Primary); 14F20, 60F10 (Secondary)."}]},{"publication":"Journal of the Institute of Mathematics of Jussieu","project":[{"call_identifier":"FWF","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","name":"New frontiers of the Manin conjecture"}],"oa_version":"Published Version","month":"11","keyword":["Integral points","del Pezzo surface","universal torsor","Manin’s conjecture"],"language":[{"iso":"eng"}],"type":"journal_article","date_published":"2022-11-10T00:00:00Z","publication_identifier":{"issn":["1474-7480"],"eissn":["1475-3030 "]},"oa":1,"main_file_link":[{"url":"https://doi.org/10.1017/S1474748022000482","open_access":"1"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","_id":"10018","author":[{"full_name":"Derenthal, Ulrich","first_name":"Ulrich","last_name":"Derenthal"},{"id":"560601DA-8D36-11E9-A136-7AC1E5697425","last_name":"Wilsch","first_name":"Florian Alexander","full_name":"Wilsch, Florian Alexander","orcid":"0000-0001-7302-8256"}],"department":[{"_id":"TiBr"}],"article_processing_charge":"Yes (via OA deal)","date_created":"2021-09-15T10:06:48Z","publication_status":"epub_ahead","title":"Integral points on singular del Pezzo surfaces","quality_controlled":"1","publisher":"Cambridge University Press","article_type":"original","year":"2022","citation":{"ista":"Derenthal U, Wilsch FA. 2022. Integral points on singular del Pezzo surfaces. Journal of the Institute of Mathematics of Jussieu.","mla":"Derenthal, Ulrich, and Florian Alexander Wilsch. “Integral Points on Singular Del Pezzo Surfaces.” Journal of the Institute of Mathematics of Jussieu, Cambridge University Press, 2022, doi:10.1017/S1474748022000482.","short":"U. Derenthal, F.A. Wilsch, Journal of the Institute of Mathematics of Jussieu (2022).","chicago":"Derenthal, Ulrich, and Florian Alexander Wilsch. “Integral Points on Singular Del Pezzo Surfaces.” Journal of the Institute of Mathematics of Jussieu. Cambridge University Press, 2022. https://doi.org/10.1017/S1474748022000482.","ieee":"U. Derenthal and F. A. Wilsch, “Integral points on singular del Pezzo surfaces,” Journal of the Institute of Mathematics of Jussieu. Cambridge University Press, 2022.","ama":"Derenthal U, Wilsch FA. Integral points on singular del Pezzo surfaces. Journal of the Institute of Mathematics of Jussieu. 2022. doi:10.1017/S1474748022000482","apa":"Derenthal, U., & Wilsch, F. A. (2022). Integral points on singular del Pezzo surfaces. Journal of the Institute of Mathematics of Jussieu. Cambridge University Press. https://doi.org/10.1017/S1474748022000482"},"date_updated":"2023-08-02T06:55:10Z","external_id":{"arxiv":["2109.06778"],"isi":["000881319200001"]},"isi":1,"day":"10","arxiv":1,"doi":"10.1017/S1474748022000482","abstract":[{"lang":"eng","text":"In order to study integral points of bounded log-anticanonical height on weak del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example, we consider a quartic del Pezzo surface of singularity type A1 + A3 and prove an analogue of Manin's conjecture for integral points with respect to its singularities and its lines."}],"acknowledgement":"The first author was partly supported by grant DE 1646/4-2 of the Deutsche Forschungsgemeinschaft. The second author was partly supported by FWF grant P 32428-N35 and conducted part of this work as a guest at the Institut de Mathématiques de Jussieu–Paris Rive Gauche invited by Antoine Chambert-Loir and funded by DAAD."},{"abstract":[{"text":"In this thesis, we study two of the most important questions in Arithmetic geometry: that of the existence and density of solutions to Diophantine equations. In order for a Diophantine equation to have any solutions over the rational numbers, it must have solutions everywhere locally, i.e., over R and over Qp for every prime p. The converse, called the Hasse principle, is known to fail in general. However, it is still a central question in Arithmetic geometry to determine for which varieties the Hasse principle does hold. In this work, we establish the Hasse principle for a wide new family of varieties of the form f(t) = NK/Q(x) ̸= 0, where f is a polynomial with integer coefficients and NK/Q denotes the norm\r\nform associated to a number field K. Our results cover products of arbitrarily many linear, quadratic or cubic factors, and generalise an argument of Irving [69], which makes use of the beta sieve of Rosser and Iwaniec. We also demonstrate how our main sieve results can be applied to treat new cases of a conjecture of Harpaz and Wittenberg on locally split values of polynomials over number fields, and discuss consequences for rational points in fibrations.\r\nIn the second question, about the density of solutions, one defines a height function and seeks to estimate asymptotically the number of points of height bounded by B as B → ∞. Traditionally, one either counts rational points, or\r\nintegral points with respect to a suitable model. However, in this thesis, we study an emerging area of interest in Arithmetic geometry known as Campana points, which in some sense interpolate between rational and integral points.\r\nMore precisely, we count the number of nonzero integers z1, z2, z3 such that gcd(z1, z2, z3) = 1, and z1, z2, z3, z1 + z2 + z3 are all squareful and bounded by B. Using the circle method, we obtain an asymptotic formula which agrees in\r\nthe power of B and log B with a bold new generalisation of Manin’s conjecture to the setting of Campana points, recently formulated by Pieropan, Smeets, Tanimoto and Várilly-Alvarado [96]. However, in this thesis we also provide the first known counterexamples to leading constant predicted by their conjecture. ","lang":"eng"}],"day":"08","doi":"10.15479/at:ista:12072","degree_awarded":"PhD","citation":{"short":"A.L. Shute, Existence and Density Problems in Diophantine Geometry: From Norm Forms to Campana Points, Institute of Science and Technology Austria, 2022.","mla":"Shute, Alec L. Existence and Density Problems in Diophantine Geometry: From Norm Forms to Campana Points. Institute of Science and Technology Austria, 2022, doi:10.15479/at:ista:12072.","ista":"Shute AL. 2022. Existence and density problems in Diophantine geometry: From norm forms to Campana points. Institute of Science and Technology Austria.","ama":"Shute AL. Existence and density problems in Diophantine geometry: From norm forms to Campana points. 2022. doi:10.15479/at:ista:12072","apa":"Shute, A. L. (2022). Existence and density problems in Diophantine geometry: From norm forms to Campana points. 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Shute, “Existence and density problems in Diophantine geometry: From norm forms to Campana points,” Institute of Science and Technology Austria, 2022."},"year":"2022","date_updated":"2023-02-21T16:37:35Z","ddc":["512"],"acknowledgement":"I acknowledge the received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska Curie Grant Agreement No. 665385.","alternative_title":["ISTA Thesis"],"title":"Existence and density problems in Diophantine geometry: From norm forms to Campana points","department":[{"_id":"GradSch"},{"_id":"TiBr"}],"date_created":"2022-09-08T21:53:03Z","article_processing_charge":"No","publication_status":"published","author":[{"id":"440EB050-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1812-2810","full_name":"Shute, Alec L","first_name":"Alec L","last_name":"Shute"}],"_id":"12072","publisher":"Institute of Science and Technology Austria","file_date_updated":"2022-09-12T11:24:21Z","ec_funded":1,"page":"208","oa":1,"supervisor":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning"}],"publication_identifier":{"issn":["2663-337X"],"isbn":["978-3-99078-023-7"]},"type":"dissertation","date_published":"2022-09-08T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)"},"related_material":{"record":[{"id":"12076","relation":"part_of_dissertation","status":"public"},{"relation":"part_of_dissertation","id":"12077","status":"public"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"file_name":"Thesis_final_draft.pdf","content_type":"application/pdf","date_updated":"2022-09-08T21:50:34Z","checksum":"bf073344320e05d92c224786cec2e92d","file_size":1907386,"date_created":"2022-09-08T21:50:34Z","creator":"ashute","file_id":"12073","relation":"main_file","access_level":"open_access","success":1},{"creator":"ashute","file_id":"12074","relation":"source_file","access_level":"closed","content_type":"application/octet-stream","file_name":"athesis.tex","date_updated":"2022-09-12T11:24:21Z","file_size":495393,"checksum":"b054ac6baa09f70e8235403a4abbed80","date_created":"2022-09-08T21:50:42Z"},{"file_size":944534,"checksum":"0a31e905f1cff5eb8110978cc90e1e79","date_created":"2022-09-09T12:05:00Z","file_name":"qfcjsfmtvtbfrjjvhdzrnqxfvgjvxtbf.zip","content_type":"application/x-zip-compressed","date_updated":"2022-09-12T11:24:21Z","relation":"source_file","access_level":"closed","creator":"ashute","file_id":"12078"}],"month":"09","project":[{"name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"oa_version":"Published Version","has_accepted_license":"1","language":[{"iso":"eng"}]},{"ddc":["510"],"volume":34,"acknowledgement":"The authors warmly thank Amos Nevo for having presented the authors to each other during\r\na beautiful conference in Goa in February 2016, where the idea of this paper was born. The\r\nfirst author thanks the IHES for two post-doctoral years when most of this paper was discussed,\r\nand the Topology team in Orsay for financial support at the final stage. The first author was\r\nsupported by the EPRSC EP/P026710/1 grant. Finally, we warmly thank the referee for many\r\nvery helpful comments that have improved the readability of this paper.","external_id":{"isi":["000926504300003"],"arxiv":["2001.01534"]},"isi":1,"year":"2022","citation":{"chicago":"Horesh, Tal, and Frédéric Paulin. “Effective Equidistribution of Lattice Points in Positive Characteristic.” Journal de Theorie Des Nombres de Bordeaux. Centre Mersenne, 2022. https://doi.org/10.5802/JTNB.1222.","ieee":"T. Horesh and F. Paulin, “Effective equidistribution of lattice points in positive characteristic,” Journal de Theorie des Nombres de Bordeaux, vol. 34, no. 3. Centre Mersenne, pp. 679–703, 2022.","ama":"Horesh T, Paulin F. Effective equidistribution of lattice points in positive characteristic. Journal de Theorie des Nombres de Bordeaux. 2022;34(3):679-703. doi:10.5802/JTNB.1222","apa":"Horesh, T., & Paulin, F. (2022). Effective equidistribution of lattice points in positive characteristic. Journal de Theorie Des Nombres de Bordeaux. Centre Mersenne. https://doi.org/10.5802/JTNB.1222","ista":"Horesh T, Paulin F. 2022. Effective equidistribution of lattice points in positive characteristic. Journal de Theorie des Nombres de Bordeaux. 34(3), 679–703.","short":"T. Horesh, F. Paulin, Journal de Theorie Des Nombres de Bordeaux 34 (2022) 679–703.","mla":"Horesh, Tal, and Frédéric Paulin. “Effective Equidistribution of Lattice Points in Positive Characteristic.” Journal de Theorie Des Nombres de Bordeaux, vol. 34, no. 3, Centre Mersenne, 2022, pp. 679–703, doi:10.5802/JTNB.1222."},"date_updated":"2023-08-04T10:41:40Z","abstract":[{"text":"Given a place ω of a global function field K over a finite field, with associated affine function ring Rω and completion Kω , the aim of this paper is to give an effective joint equidistribution result for renormalized primitive lattice points (a,b)∈Rω2 in the plane Kω2 , and for renormalized solutions to the gcd equation ax+by=1 . The main tools are techniques of Goronik and Nevo for counting lattice points in well-rounded families of subsets. This gives a sharper analog in positive characteristic of a result of Nevo and the first author for the equidistribution of the primitive lattice points in \\ZZ2 .","lang":"eng"}],"day":"27","doi":"10.5802/JTNB.1222","arxiv":1,"file_date_updated":"2023-02-27T09:10:13Z","quality_controlled":"1","page":"679-703","article_type":"original","publisher":"Centre Mersenne","issue":"3","author":[{"id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425","first_name":"Tal","last_name":"Horesh","full_name":"Horesh, Tal"},{"first_name":"Frédéric","last_name":"Paulin","full_name":"Paulin, Frédéric"}],"scopus_import":"1","_id":"12684","intvolume":" 34","title":"Effective equidistribution of lattice points in positive characteristic","date_created":"2023-02-26T23:01:02Z","department":[{"_id":"TiBr"}],"article_processing_charge":"No","publication_status":"published","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"checksum":"08f28fded270251f568f610cf5166d69","file_size":870468,"date_created":"2023-02-27T09:10:13Z","file_name":"2023_JourTheorieNombreBordeaux_Horesh.pdf","content_type":"application/pdf","date_updated":"2023-02-27T09:10:13Z","success":1,"access_level":"open_access","relation":"main_file","creator":"dernst","file_id":"12689"}],"type":"journal_article","date_published":"2022-01-27T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)"},"oa":1,"publication_identifier":{"issn":["1246-7405"],"eissn":["2118-8572"]},"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Journal de Theorie des Nombres de Bordeaux","month":"01","oa_version":"Published Version"},{"day":"24","abstract":[{"text":"An improved asymptotic formula is established for the number of rational points of bounded height on the split smooth del Pezzo surface of degree 5. The proof uses the five conic bundle structures on the surface.","lang":"eng"}],"citation":{"chicago":"Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split Del Pezzo Surface of Degree 5.” New York Journal of Mathematics. State University of New York, 2022.","ieee":"T. D. Browning, “Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5,” New York Journal of Mathematics, vol. 28. State University of New York, pp. 1193–1229, 2022.","apa":"Browning, T. D. (2022). Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. New York Journal of Mathematics. State University of New York.","ama":"Browning TD. Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. New York Journal of Mathematics. 2022;28:1193-1229.","ista":"Browning TD. 2022. Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. New York Journal of Mathematics. 28, 1193–1229.","short":"T.D. Browning, New York Journal of Mathematics 28 (2022) 1193–1229.","mla":"Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split Del Pezzo Surface of Degree 5.” New York Journal of Mathematics, vol. 28, State University of New York, 2022, pp. 1193–229."},"year":"2022","date_updated":"2023-10-18T07:59:13Z","acknowledgement":"This work was begun while the author was participating in the programme on \"Diophantine equations\" at the Hausdorff Research Institute for Mathematics in Bonn in 2009. The hospitality and financial support of the institute is gratefully acknowledged. The idea of using conic bundles to study the split del Pezzo surface of degree 5 was explained to the author by Professor Salberger. The author is very grateful to him for his input into this project and also to Shuntaro Yamagishi for many useful comments on an earlier version of this manuscript. While working on this paper the author was supported by FWF grant P32428-N35.","volume":28,"ddc":["510"],"department":[{"_id":"TiBr"}],"date_created":"2023-03-28T09:21:09Z","article_processing_charge":"No","publication_status":"published","intvolume":" 28","title":"Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5","_id":"12776","author":[{"orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87"}],"publisher":"State University of New York","article_type":"original","quality_controlled":"1","page":"1193 - 1229","file_date_updated":"2023-03-30T07:09:35Z","publication_identifier":{"issn":["1076-9803"]},"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2022-08-24T00:00:00Z","file":[{"file_id":"12778","creator":"dernst","success":1,"access_level":"open_access","relation":"main_file","date_updated":"2023-03-30T07:09:35Z","file_name":"2022_NYJM_Browning.pdf","content_type":"application/pdf","date_created":"2023-03-30T07:09:35Z","file_size":897267,"checksum":"c01e8291794a1bdb7416aa103cb68ef8"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"call_identifier":"FWF","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","name":"New frontiers of the Manin conjecture","grant_number":"P32428"}],"oa_version":"Published Version","month":"08","has_accepted_license":"1","publication":"New York Journal of Mathematics","language":[{"iso":"eng"}]}]