[{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1909.03266"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["0010-437X"],"eissn":["1570-5846"]},"oa":1,"date_published":"2021-06-28T00:00:00Z","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"oa_version":"Preprint","month":"06","publication":"Compositio Mathematica","volume":157,"acknowledgement":"We would like to thank the anonymous referees for carefully reading the paper and for their remarks and suggestions.","doi":"10.1112/s0010437x21007351","arxiv":1,"day":"28","abstract":[{"lang":"eng","text":"In this paper, we investigate the distribution of the maximum of partial sums of families of  m -periodic complex-valued functions satisfying certain conditions. We obtain precise uniform estimates for the distribution function of this maximum in a near-optimal range. Our results apply to partial sums of Kloosterman sums and other families of  ℓ -adic trace functions, and are as strong as those obtained by Bober, Goldmakher, Granville and Koukoulopoulos for character sums. In particular, we improve on the recent work of the third author for Birch sums. However, unlike character sums, we are able to construct families of  m -periodic complex-valued functions which satisfy our conditions, but for which the Pólya–Vinogradov inequality is sharp."}],"date_updated":"2023-08-17T06:59:16Z","citation":{"ista":"Autissier P, Bonolis D, Lamzouri Y. 2021. The distribution of the maximum of partial sums of Kloosterman sums and other trace functions. Compositio Mathematica. 157(7), 1610–1651.","short":"P. Autissier, D. Bonolis, Y. Lamzouri, Compositio Mathematica 157 (2021) 1610–1651.","mla":"Autissier, Pascal, et al. “The Distribution of the Maximum of Partial Sums of Kloosterman Sums and Other Trace Functions.” <i>Compositio Mathematica</i>, vol. 157, no. 7, Cambridge University Press, 2021, pp. 1610–51, doi:<a href=\"https://doi.org/10.1112/s0010437x21007351\">10.1112/s0010437x21007351</a>.","chicago":"Autissier, Pascal, Dante Bonolis, and Youness Lamzouri. “The Distribution of the Maximum of Partial Sums of Kloosterman Sums and Other Trace Functions.” <i>Compositio Mathematica</i>. Cambridge University Press, 2021. <a href=\"https://doi.org/10.1112/s0010437x21007351\">https://doi.org/10.1112/s0010437x21007351</a>.","ieee":"P. Autissier, D. Bonolis, and Y. Lamzouri, “The distribution of the maximum of partial sums of Kloosterman sums and other trace functions,” <i>Compositio Mathematica</i>, vol. 157, no. 7. Cambridge University Press, pp. 1610–1651, 2021.","ama":"Autissier P, Bonolis D, Lamzouri Y. The distribution of the maximum of partial sums of Kloosterman sums and other trace functions. <i>Compositio Mathematica</i>. 2021;157(7):1610-1651. doi:<a href=\"https://doi.org/10.1112/s0010437x21007351\">10.1112/s0010437x21007351</a>","apa":"Autissier, P., Bonolis, D., &#38; Lamzouri, Y. (2021). The distribution of the maximum of partial sums of Kloosterman sums and other trace functions. <i>Compositio Mathematica</i>. Cambridge University Press. <a href=\"https://doi.org/10.1112/s0010437x21007351\">https://doi.org/10.1112/s0010437x21007351</a>"},"year":"2021","isi":1,"external_id":{"isi":["000667289300001"],"arxiv":["1909.03266"]},"publisher":"Cambridge University Press","article_type":"original","page":"1610-1651","quality_controlled":"1","publication_status":"published","department":[{"_id":"TiBr"}],"date_created":"2022-02-01T08:10:43Z","article_processing_charge":"No","title":"The distribution of the maximum of partial sums of Kloosterman sums and other trace functions","intvolume":"       157","_id":"10711","author":[{"full_name":"Autissier, Pascal","first_name":"Pascal","last_name":"Autissier"},{"id":"6A459894-5FDD-11E9-AF35-BB24E6697425","first_name":"Dante","last_name":"Bonolis","full_name":"Bonolis, Dante"},{"last_name":"Lamzouri","first_name":"Youness","full_name":"Lamzouri, Youness"}],"issue":"7"},{"article_type":"original","publisher":"De Gruyter","page":"147-165","quality_controlled":"1","title":"The geometric sieve for quadrics","intvolume":"        33","publication_status":"published","department":[{"_id":"TiBr"}],"date_created":"2020-11-08T23:01:25Z","article_processing_charge":"No","author":[{"orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Roger","last_name":"Heath-Brown","full_name":"Heath-Brown, Roger"}],"issue":"1","_id":"8742","scopus_import":"1","volume":33,"abstract":[{"text":"We develop a version of Ekedahl’s geometric sieve for integral quadratic forms of rank at least five. As one ranges over the zeros of such quadratic forms, we use the sieve to compute the density of coprime values of polynomials, and furthermore, to address a question about local solubility in families of varieties parameterised by the zeros.","lang":"eng"}],"doi":"10.1515/forum-2020-0074","arxiv":1,"day":"01","isi":1,"external_id":{"isi":["000604750900008"],"arxiv":["2003.09593"]},"date_updated":"2023-10-17T07:39:01Z","citation":{"ieee":"T. D. Browning and R. Heath-Brown, “The geometric sieve for quadrics,” <i>Forum Mathematicum</i>, vol. 33, no. 1. De Gruyter, pp. 147–165, 2021.","chicago":"Browning, Timothy D, and Roger Heath-Brown. “The Geometric Sieve for Quadrics.” <i>Forum Mathematicum</i>. De Gruyter, 2021. <a href=\"https://doi.org/10.1515/forum-2020-0074\">https://doi.org/10.1515/forum-2020-0074</a>.","apa":"Browning, T. D., &#38; Heath-Brown, R. (2021). The geometric sieve for quadrics. <i>Forum Mathematicum</i>. De Gruyter. <a href=\"https://doi.org/10.1515/forum-2020-0074\">https://doi.org/10.1515/forum-2020-0074</a>","ama":"Browning TD, Heath-Brown R. The geometric sieve for quadrics. <i>Forum Mathematicum</i>. 2021;33(1):147-165. doi:<a href=\"https://doi.org/10.1515/forum-2020-0074\">10.1515/forum-2020-0074</a>","ista":"Browning TD, Heath-Brown R. 2021. The geometric sieve for quadrics. Forum Mathematicum. 33(1), 147–165.","mla":"Browning, Timothy D., and Roger Heath-Brown. “The Geometric Sieve for Quadrics.” <i>Forum Mathematicum</i>, vol. 33, no. 1, De Gruyter, 2021, pp. 147–65, doi:<a href=\"https://doi.org/10.1515/forum-2020-0074\">10.1515/forum-2020-0074</a>.","short":"T.D. Browning, R. Heath-Brown, Forum Mathematicum 33 (2021) 147–165."},"year":"2021","language":[{"iso":"eng"}],"month":"01","oa_version":"Preprint","project":[{"grant_number":"P32428","name":"New frontiers of the Manin conjecture","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"publication":"Forum Mathematicum","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2003.09593"}],"oa":1,"publication_identifier":{"eissn":["1435-5337"],"issn":["0933-7741"]},"date_published":"2021-01-01T00:00:00Z","type":"journal_article"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","file":[{"date_updated":"2021-03-22T12:41:26Z","content_type":"application/pdf","file_name":"2021_MathZeitschrift_Browning.pdf","date_created":"2021-03-22T12:41:26Z","file_size":492685,"checksum":"8ed9f49568806894744096dbbca0ad7b","file_id":"9279","creator":"dernst","access_level":"open_access","success":1,"relation":"main_file"}],"date_published":"2021-03-05T00:00:00Z","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":["1432-1823"],"issn":["0025-5874"]},"language":[{"iso":"eng"}],"publication":"Mathematische Zeitschrift","has_accepted_license":"1","month":"03","oa_version":"Published Version","project":[{"_id":"26A8D266-B435-11E9-9278-68D0E5697425","name":"Between rational and integral points","grant_number":"EP-P026710-2"}],"ddc":["510"],"volume":299,"acknowledgement":"While working on this paper the authors were both supported by EPSRC grant EP/P026710/1, and the second author received additional support from the NWO Veni Grant 016.Veni.192.047. Thanks are due to Marta Pieropan, Arne Smeets and Sho Tanimoto for useful conversations related to this topic, and to the anonymous referee for numerous helpful suggestions.","isi":1,"external_id":{"isi":["000625573800002"]},"date_updated":"2023-08-07T14:20:00Z","citation":{"ista":"Browning TD, Yamagishi S. 2021. Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. Mathematische Zeitschrift. 299, 1071–1101.","short":"T.D. Browning, S. Yamagishi, Mathematische Zeitschrift 299 (2021) 1071–1101.","mla":"Browning, Timothy D., and Shuntaro Yamagishi. “Arithmetic of Higher-Dimensional Orbifolds and a Mixed Waring Problem.” <i>Mathematische Zeitschrift</i>, vol. 299, Springer Nature, 2021, pp. 1071–1101, doi:<a href=\"https://doi.org/10.1007/s00209-021-02695-w\">10.1007/s00209-021-02695-w</a>.","ieee":"T. D. Browning and S. Yamagishi, “Arithmetic of higher-dimensional orbifolds and a mixed Waring problem,” <i>Mathematische Zeitschrift</i>, vol. 299. Springer Nature, pp. 1071–1101, 2021.","chicago":"Browning, Timothy D, and Shuntaro Yamagishi. “Arithmetic of Higher-Dimensional Orbifolds and a Mixed Waring Problem.” <i>Mathematische Zeitschrift</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00209-021-02695-w\">https://doi.org/10.1007/s00209-021-02695-w</a>.","apa":"Browning, T. D., &#38; Yamagishi, S. (2021). Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. <i>Mathematische Zeitschrift</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00209-021-02695-w\">https://doi.org/10.1007/s00209-021-02695-w</a>","ama":"Browning TD, Yamagishi S. Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. <i>Mathematische Zeitschrift</i>. 2021;299:1071–1101. doi:<a href=\"https://doi.org/10.1007/s00209-021-02695-w\">10.1007/s00209-021-02695-w</a>"},"year":"2021","abstract":[{"text":"We study the density of rational points on a higher-dimensional orbifold (Pn−1,Δ) when Δ is a Q-divisor involving hyperplanes. This allows us to address a question of Tanimoto about whether the set of rational points on such an orbifold constitutes a thin set. Our approach relies on the Hardy–Littlewood circle method to first study an asymptotic version of Waring’s problem for mixed powers. In doing so we make crucial use of the recent resolution of the main conjecture in Vinogradov’s mean value theorem, due to Bourgain–Demeter–Guth and Wooley.","lang":"eng"}],"doi":"10.1007/s00209-021-02695-w","day":"05","file_date_updated":"2021-03-22T12:41:26Z","page":"1071–1101","quality_controlled":"1","article_type":"original","publisher":"Springer Nature","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":"Yamagishi, Shuntaro","last_name":"Yamagishi","first_name":"Shuntaro"}],"_id":"9260","scopus_import":"1","title":"Arithmetic of higher-dimensional orbifolds and a mixed Waring problem","intvolume":"       299","publication_status":"published","date_created":"2021-03-21T23:01:21Z","department":[{"_id":"TiBr"}],"article_processing_charge":"No"},{"page":"XIV, 166","quality_controlled":"1","language":[{"iso":"eng"}],"publisher":"Springer Nature","_id":"10415","scopus_import":"1","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","last_name":"Browning","first_name":"Timothy D"}],"oa_version":"None","publication_status":"published","date_created":"2021-12-05T23:01:46Z","article_processing_charge":"No","department":[{"_id":"TiBr"}],"alternative_title":["Progress in Mathematics"],"month":"12","title":"Cubic Forms and the Circle Method","intvolume":"       343","volume":343,"place":"Cham","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2022-06-03T07:38:33Z","year":"2021","citation":{"short":"T.D. Browning, Cubic Forms and the Circle Method, Springer Nature, Cham, 2021.","mla":"Browning, Timothy D. <i>Cubic Forms and the Circle Method</i>. Vol. 343, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/978-3-030-86872-7\">10.1007/978-3-030-86872-7</a>.","ista":"Browning TD. 2021. Cubic Forms and the Circle Method, Cham: Springer Nature, XIV, 166p.","ama":"Browning TD. <i>Cubic Forms and the Circle Method</i>. Vol 343. Cham: Springer Nature; 2021. doi:<a href=\"https://doi.org/10.1007/978-3-030-86872-7\">10.1007/978-3-030-86872-7</a>","apa":"Browning, T. D. (2021). <i>Cubic Forms and the Circle Method</i> (Vol. 343). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-86872-7\">https://doi.org/10.1007/978-3-030-86872-7</a>","chicago":"Browning, Timothy D. <i>Cubic Forms and the Circle Method</i>. Vol. 343. Cham: Springer Nature, 2021. <a href=\"https://doi.org/10.1007/978-3-030-86872-7\">https://doi.org/10.1007/978-3-030-86872-7</a>.","ieee":"T. D. Browning, <i>Cubic Forms and the Circle Method</i>, vol. 343. Cham: Springer Nature, 2021."},"date_published":"2021-12-01T00:00:00Z","type":"book","doi":"10.1007/978-3-030-86872-7","publication_identifier":{"isbn":["978-3-030-86871-0"],"issn":["0743-1643"],"eissn":["2296-505X"],"eisbn":["978-3-030-86872-7"]},"day":"01","abstract":[{"lang":"eng","text":"The Hardy–Littlewood circle method was invented over a century ago to study integer solutions to special Diophantine equations, but it has since proven to be one of the most successful all-purpose tools available to number theorists. Not only is it capable of handling remarkably general systems of polynomial equations defined over arbitrary global fields, but it can also shed light on the space of rational curves that lie on algebraic varieties.  This book, in which the arithmetic of cubic polynomials takes centre stage, is aimed at bringing beginning graduate students into contact with some of the many facets of the circle method, both classical and modern. This monograph is the winner of the 2021 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics."}]},{"language":[{"iso":"eng"}],"author":[{"id":"440EB050-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1812-2810","full_name":"Shute, Alec L","first_name":"Alec L","last_name":"Shute"}],"publication":"arXiv","_id":"12076","article_number":"2104.06966","month":"04","title":"Sums of four squareful numbers","department":[{"_id":"TiBr"}],"article_processing_charge":"No","date_created":"2022-09-09T10:42:51Z","oa_version":"Preprint","publication_status":"submitted","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"relation":"dissertation_contains","id":"12072","status":"public"}]},"status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2104.06966"}],"external_id":{"arxiv":["2104.06966"]},"type":"preprint","date_published":"2021-04-15T00:00:00Z","citation":{"ista":"Shute AL. Sums of four squareful numbers. arXiv, 2104.06966.","short":"A.L. Shute, ArXiv (n.d.).","mla":"Shute, Alec L. “Sums of Four Squareful Numbers.” <i>ArXiv</i>, 2104.06966, doi:<a href=\"https://doi.org/10.48550/arXiv.2104.06966\">10.48550/arXiv.2104.06966</a>.","chicago":"Shute, Alec L. “Sums of Four Squareful Numbers.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2104.06966\">https://doi.org/10.48550/arXiv.2104.06966</a>.","ieee":"A. L. Shute, “Sums of four squareful numbers,” <i>arXiv</i>. .","ama":"Shute AL. Sums of four squareful numbers. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2104.06966\">10.48550/arXiv.2104.06966</a>","apa":"Shute, A. L. (n.d.). Sums of four squareful numbers. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2104.06966\">https://doi.org/10.48550/arXiv.2104.06966</a>"},"year":"2021","date_updated":"2023-02-21T16:37:30Z","oa":1,"abstract":[{"text":"We find an asymptotic formula for the number of primitive vectors $(z_1,\\ldots,z_4)\\in (\\mathbb{Z}_{\\neq 0})^4$ such that $z_1,\\ldots, z_4$ are all squareful and bounded by $B$, and $z_1+\\cdots + z_4 = 0$. Our result agrees in the power of $B$ and $\\log B$ with the Campana-Manin conjecture of Pieropan, Smeets, Tanimoto and V\\'{a}rilly-Alvarado.","lang":"eng"}],"day":"15","doi":"10.48550/arXiv.2104.06966","arxiv":1},{"language":[{"iso":"eng"}],"oa_version":"Preprint","publication_status":"submitted","date_created":"2022-09-09T10:43:17Z","article_processing_charge":"No","department":[{"_id":"TiBr"}],"month":"04","title":"On the leading constant in the Manin-type conjecture for Campana points","article_number":"2104.14946","_id":"12077","publication":"arXiv","author":[{"id":"440EB050-F248-11E8-B48F-1D18A9856A87","last_name":"Shute","first_name":"Alec L","full_name":"Shute, Alec L","orcid":"0000-0002-1812-2810"}],"acknowledgement":"The author would like to thank Damaris Schindler and Florian Wilsch for their helpful comments on the heights and Tamagawa measures used in Section 3, together with Marta Pieropan, Sho Tanimoto and Sam Streeter for providing valuable feedback on an earlier version of this paper, and Tim Browning for many useful comments and discussions during the development of this work. The author is also grateful to the anonymous referee for providing many valuable comments and suggestions that improved the quality of the paper.","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2104.14946"}],"related_material":{"record":[{"id":"12072","relation":"dissertation_contains","status":"public"}]},"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"doi":"10.48550/arXiv.2104.14946","day":"30","abstract":[{"text":"We compare the Manin-type conjecture for Campana points recently formulated\r\nby Pieropan, Smeets, Tanimoto and V\\'{a}rilly-Alvarado with an alternative\r\nprediction of Browning and Van Valckenborgh in the special case of the orbifold\r\n$(\\mathbb{P}^1,D)$, where $D =\\frac{1}{2}[0]+\\frac{1}{2}[1]+\\frac{1}{2}[\\infty]$. We find that the two predicted leading constants do not agree, and we discuss whether thin sets\r\ncould explain this discrepancy. Motivated by this, we provide a counterexample\r\nto the Manin-type conjecture for Campana points, by considering orbifolds\r\ncorresponding to squareful values of binary quadratic forms.","lang":"eng"}],"oa":1,"date_updated":"2023-02-21T16:37:30Z","year":"2021","citation":{"apa":"Shute, A. L. (n.d.). On the leading constant in the Manin-type conjecture for Campana points. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2104.14946\">https://doi.org/10.48550/arXiv.2104.14946</a>","ama":"Shute AL. On the leading constant in the Manin-type conjecture for Campana points. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2104.14946\">10.48550/arXiv.2104.14946</a>","ieee":"A. L. Shute, “On the leading constant in the Manin-type conjecture for Campana points,” <i>arXiv</i>. .","chicago":"Shute, Alec L. “On the Leading Constant in the Manin-Type Conjecture for Campana Points.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2104.14946\">https://doi.org/10.48550/arXiv.2104.14946</a>.","short":"A.L. Shute, ArXiv (n.d.).","mla":"Shute, Alec L. “On the Leading Constant in the Manin-Type Conjecture for Campana Points.” <i>ArXiv</i>, 2104.14946, doi:<a href=\"https://doi.org/10.48550/arXiv.2104.14946\">10.48550/arXiv.2104.14946</a>.","ista":"Shute AL. On the leading constant in the Manin-type conjecture for Campana points. arXiv, 2104.14946."},"date_published":"2021-04-30T00:00:00Z","external_id":{"arxiv":["2104.14946"]},"type":"preprint"},{"publication":"Annals of Mathematics","month":"05","oa_version":"Preprint","language":[{"iso":"eng"}],"type":"journal_article","date_published":"2020-05-01T00:00:00Z","publist_id":"7744","oa":1,"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"url":"https://arxiv.org/abs/1711.10451","open_access":"1"}],"issue":"3","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning"},{"full_name":"Sawin, Will","first_name":"Will","last_name":"Sawin"}],"_id":"177","intvolume":"       191","title":"A geometric version of the circle method","department":[{"_id":"TiBr"}],"date_created":"2018-12-11T11:45:02Z","article_processing_charge":"No","publication_status":"published","quality_controlled":"1","page":"893-948","article_type":"original","publisher":"Princeton University","external_id":{"isi":["000526986300004"],"arxiv":["1711.10451"]},"isi":1,"year":"2020","citation":{"ista":"Browning TD, Sawin W. 2020. A geometric version of the circle method. Annals of Mathematics. 191(3), 893–948.","short":"T.D. Browning, W. Sawin, Annals of Mathematics 191 (2020) 893–948.","mla":"Browning, Timothy D., and Will Sawin. “A Geometric Version of the Circle Method.” <i>Annals of Mathematics</i>, vol. 191, no. 3, Princeton University, 2020, pp. 893–948, doi:<a href=\"https://doi.org/10.4007/annals.2020.191.3.4\">10.4007/annals.2020.191.3.4</a>.","ieee":"T. D. Browning and W. Sawin, “A geometric version of the circle method,” <i>Annals of Mathematics</i>, vol. 191, no. 3. Princeton University, pp. 893–948, 2020.","chicago":"Browning, Timothy D, and Will Sawin. “A Geometric Version of the Circle Method.” <i>Annals of Mathematics</i>. Princeton University, 2020. <a href=\"https://doi.org/10.4007/annals.2020.191.3.4\">https://doi.org/10.4007/annals.2020.191.3.4</a>.","apa":"Browning, T. D., &#38; Sawin, W. (2020). A geometric version of the circle method. <i>Annals of Mathematics</i>. Princeton University. <a href=\"https://doi.org/10.4007/annals.2020.191.3.4\">https://doi.org/10.4007/annals.2020.191.3.4</a>","ama":"Browning TD, Sawin W. A geometric version of the circle method. <i>Annals of Mathematics</i>. 2020;191(3):893-948. doi:<a href=\"https://doi.org/10.4007/annals.2020.191.3.4\">10.4007/annals.2020.191.3.4</a>"},"date_updated":"2023-08-17T07:12:37Z","abstract":[{"lang":"eng","text":"We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree."}],"day":"01","arxiv":1,"doi":"10.4007/annals.2020.191.3.4","volume":191},{"article_type":"original","publisher":"Duke University Press","quality_controlled":"1","page":"3099-3165","intvolume":"       169","title":"Density of rational points on a quadric bundle in ℙ3×ℙ3","department":[{"_id":"TiBr"}],"article_processing_charge":"No","date_created":"2018-12-11T11:45:02Z","publication_status":"published","issue":"16","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning"},{"first_name":"Roger","last_name":"Heath Brown","full_name":"Heath Brown, Roger"}],"_id":"179","volume":169,"abstract":[{"lang":"eng","text":"An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface x1y21+⋯+x4y24=0 in ℙ3×ℙ3. This confirms the modified Manin conjecture for this variety, in which the removal of a thin set of rational points is allowed."}],"day":"10","arxiv":1,"doi":"10.1215/00127094-2020-0031","external_id":{"arxiv":["1805.10715"],"isi":["000582676300002"]},"isi":1,"citation":{"ieee":"T. D. Browning and R. Heath Brown, “Density of rational points on a quadric bundle in ℙ3×ℙ3,” <i>Duke Mathematical Journal</i>, vol. 169, no. 16. Duke University Press, pp. 3099–3165, 2020.","chicago":"Browning, Timothy D, and Roger Heath Brown. “Density of Rational Points on a Quadric Bundle in ℙ3×ℙ3.” <i>Duke Mathematical Journal</i>. Duke University Press, 2020. <a href=\"https://doi.org/10.1215/00127094-2020-0031\">https://doi.org/10.1215/00127094-2020-0031</a>.","ama":"Browning TD, Heath Brown R. Density of rational points on a quadric bundle in ℙ3×ℙ3. <i>Duke Mathematical Journal</i>. 2020;169(16):3099-3165. doi:<a href=\"https://doi.org/10.1215/00127094-2020-0031\">10.1215/00127094-2020-0031</a>","apa":"Browning, T. D., &#38; Heath Brown, R. (2020). Density of rational points on a quadric bundle in ℙ3×ℙ3. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/00127094-2020-0031\">https://doi.org/10.1215/00127094-2020-0031</a>","ista":"Browning TD, Heath Brown R. 2020. Density of rational points on a quadric bundle in ℙ3×ℙ3. Duke Mathematical Journal. 169(16), 3099–3165.","mla":"Browning, Timothy D., and Roger Heath Brown. “Density of Rational Points on a Quadric Bundle in ℙ3×ℙ3.” <i>Duke Mathematical Journal</i>, vol. 169, no. 16, Duke University Press, 2020, pp. 3099–165, doi:<a href=\"https://doi.org/10.1215/00127094-2020-0031\">10.1215/00127094-2020-0031</a>.","short":"T.D. Browning, R. Heath Brown, Duke Mathematical Journal 169 (2020) 3099–3165."},"year":"2020","date_updated":"2023-10-17T12:51:10Z","language":[{"iso":"eng"}],"month":"09","oa_version":"Preprint","publication":"Duke Mathematical Journal","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","main_file_link":[{"url":"https://arxiv.org/abs/1805.10715","open_access":"1"}],"oa":1,"publication_identifier":{"issn":["0012-7094"]},"type":"journal_article","date_published":"2020-09-10T00:00:00Z"},{"issue":"4","author":[{"first_name":"Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Will","last_name":"Sawin","full_name":"Sawin, Will"}],"scopus_import":"1","_id":"9007","intvolume":"        95","title":"Free rational points on smooth hypersurfaces","date_created":"2021-01-17T23:01:11Z","article_processing_charge":"No","department":[{"_id":"TiBr"}],"publication_status":"published","quality_controlled":"1","page":"635-659","article_type":"original","publisher":"European Mathematical Society","external_id":{"arxiv":["1906.08463"],"isi":["000596833300001"]},"isi":1,"citation":{"chicago":"Browning, Timothy D, and Will Sawin. “Free Rational Points on Smooth Hypersurfaces.” <i>Commentarii Mathematici Helvetici</i>. European Mathematical Society, 2020. <a href=\"https://doi.org/10.4171/CMH/499\">https://doi.org/10.4171/CMH/499</a>.","ieee":"T. D. Browning and W. Sawin, “Free rational points on smooth hypersurfaces,” <i>Commentarii Mathematici Helvetici</i>, vol. 95, no. 4. European Mathematical Society, pp. 635–659, 2020.","apa":"Browning, T. D., &#38; Sawin, W. (2020). Free rational points on smooth hypersurfaces. <i>Commentarii Mathematici Helvetici</i>. European Mathematical Society. <a href=\"https://doi.org/10.4171/CMH/499\">https://doi.org/10.4171/CMH/499</a>","ama":"Browning TD, Sawin W. Free rational points on smooth hypersurfaces. <i>Commentarii Mathematici Helvetici</i>. 2020;95(4):635-659. doi:<a href=\"https://doi.org/10.4171/CMH/499\">10.4171/CMH/499</a>","ista":"Browning TD, Sawin W. 2020. Free rational points on smooth hypersurfaces. Commentarii Mathematici Helvetici. 95(4), 635–659.","mla":"Browning, Timothy D., and Will Sawin. “Free Rational Points on Smooth Hypersurfaces.” <i>Commentarii Mathematici Helvetici</i>, vol. 95, no. 4, European Mathematical Society, 2020, pp. 635–59, doi:<a href=\"https://doi.org/10.4171/CMH/499\">10.4171/CMH/499</a>.","short":"T.D. Browning, W. Sawin, Commentarii Mathematici Helvetici 95 (2020) 635–659."},"year":"2020","date_updated":"2023-08-24T11:11:36Z","abstract":[{"text":"Motivated by a recent question of Peyre, we apply the Hardy–Littlewood circle method to count “sufficiently free” rational points of bounded height on arbitrary smooth projective hypersurfaces of low degree that are defined over the rationals.","lang":"eng"}],"day":"07","arxiv":1,"doi":"10.4171/CMH/499","volume":95,"publication":"Commentarii Mathematici Helvetici","month":"12","oa_version":"Preprint","language":[{"iso":"eng"}],"type":"journal_article","date_published":"2020-12-07T00:00:00Z","oa":1,"publication_identifier":{"issn":["00102571"],"eissn":["14208946"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1906.08463"}]},{"keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"oa_version":"Preprint","article_number":"9","month":"01","publication":"Research in Number Theory","main_file_link":[{"url":"https://arxiv.org/abs/1807.08986","open_access":"1"}],"status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publication_identifier":{"issn":["2522-0160"],"eissn":["2363-9555"]},"oa":1,"type":"journal_article","date_published":"2019-01-02T00:00:00Z","publisher":"Springer Nature","article_type":"original","quality_controlled":"1","article_processing_charge":"No","date_created":"2022-03-18T12:09:48Z","department":[{"_id":"TiBr"}],"publication_status":"published","intvolume":"         5","title":"Modular invariants for genus 3 hyperelliptic curves","scopus_import":"1","_id":"10874","author":[{"full_name":"Ionica, Sorina","last_name":"Ionica","first_name":"Sorina"},{"first_name":"Pınar","last_name":"Kılıçer","full_name":"Kılıçer, Pınar"},{"last_name":"Lauter","first_name":"Kristin","full_name":"Lauter, Kristin"},{"full_name":"Lorenzo García, Elisa","first_name":"Elisa","last_name":"Lorenzo García"},{"last_name":"Manzateanu","first_name":"Maria-Adelina","full_name":"Manzateanu, Maria-Adelina","id":"be8d652e-a908-11ec-82a4-e2867729459c"},{"full_name":"Massierer, Maike","first_name":"Maike","last_name":"Massierer"},{"full_name":"Vincent, Christelle","last_name":"Vincent","first_name":"Christelle"}],"acknowledgement":"The authors would like to thank the Lorentz Center in Leiden for hosting the Women in Numbers Europe 2 workshop and providing a productive and enjoyable environment for our initial work on this project. We are grateful to the organizers of WIN-E2, Irene Bouw, Rachel Newton and Ekin Ozman, for making this conference and this collaboration possible. We\r\nthank Irene Bouw and Christophe Ritzenhaler for helpful discussions. Ionica acknowledges support from the Thomas Jefferson Fund of the Embassy of France in the United States and the FACE Foundation. Most of Kılıçer’s work was carried out during her stay in Universiteit Leiden and Carl von Ossietzky Universität Oldenburg. Massierer was supported by the Australian Research Council (DP150101689). Vincent is supported by the National Science Foundation under Grant No. DMS-1802323 and by the Thomas Jefferson Fund of the Embassy of France in the United States and the FACE Foundation. ","volume":5,"day":"02","doi":"10.1007/s40993-018-0146-6","arxiv":1,"abstract":[{"text":"In this article we prove an analogue of a theorem of Lachaud, Ritzenthaler, and Zykin, which allows us to connect invariants of binary octics to Siegel modular forms of genus 3. We use this connection to show that certain modular functions, when restricted to the hyperelliptic locus, assume values whose denominators are products of powers of primes of bad reduction for the associated hyperelliptic curves. We illustrate our theorem with explicit computations. This work is motivated by the study of the values of these modular functions at CM points of the Siegel upper half-space, which, if their denominators are known, can be used to effectively compute models of (hyperelliptic, in our case) curves with CM.","lang":"eng"}],"year":"2019","citation":{"ista":"Ionica S, Kılıçer P, Lauter K, Lorenzo García E, Manzateanu M-A, Massierer M, Vincent C. 2019. Modular invariants for genus 3 hyperelliptic curves. Research in Number Theory. 5, 9.","short":"S. Ionica, P. Kılıçer, K. Lauter, E. Lorenzo García, M.-A. Manzateanu, M. Massierer, C. Vincent, Research in Number Theory 5 (2019).","mla":"Ionica, Sorina, et al. “Modular Invariants for Genus 3 Hyperelliptic Curves.” <i>Research in Number Theory</i>, vol. 5, 9, Springer Nature, 2019, doi:<a href=\"https://doi.org/10.1007/s40993-018-0146-6\">10.1007/s40993-018-0146-6</a>.","chicago":"Ionica, Sorina, Pınar Kılıçer, Kristin Lauter, Elisa Lorenzo García, Maria-Adelina Manzateanu, Maike Massierer, and Christelle Vincent. “Modular Invariants for Genus 3 Hyperelliptic Curves.” <i>Research in Number Theory</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s40993-018-0146-6\">https://doi.org/10.1007/s40993-018-0146-6</a>.","ieee":"S. Ionica <i>et al.</i>, “Modular invariants for genus 3 hyperelliptic curves,” <i>Research in Number Theory</i>, vol. 5. Springer Nature, 2019.","apa":"Ionica, S., Kılıçer, P., Lauter, K., Lorenzo García, E., Manzateanu, M.-A., Massierer, M., &#38; Vincent, C. (2019). Modular invariants for genus 3 hyperelliptic curves. <i>Research in Number Theory</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40993-018-0146-6\">https://doi.org/10.1007/s40993-018-0146-6</a>","ama":"Ionica S, Kılıçer P, Lauter K, et al. Modular invariants for genus 3 hyperelliptic curves. <i>Research in Number Theory</i>. 2019;5. doi:<a href=\"https://doi.org/10.1007/s40993-018-0146-6\">10.1007/s40993-018-0146-6</a>"},"date_updated":"2023-09-05T15:39:31Z","external_id":{"arxiv":["1807.08986"]}},{"language":[{"iso":"eng"}],"month":"04","oa_version":"Preprint","publication":"Transactions of the American Mathematical Society","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.01999"}],"oa":1,"publist_id":"7746","publication_identifier":{"eissn":["10886850"],"issn":["00029947"]},"date_published":"2019-04-15T00:00:00Z","type":"journal_article","publisher":"American Mathematical Society","page":"5757-5785","quality_controlled":"1","title":"Sieving rational points on varieties","intvolume":"       371","publication_status":"published","date_created":"2018-12-11T11:45:01Z","department":[{"_id":"TiBr"}],"article_processing_charge":"No","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","first_name":"Timothy D","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177"},{"last_name":"Loughran","first_name":"Daniel","full_name":"Loughran, Daniel"}],"issue":"8","_id":"175","scopus_import":"1","volume":371,"abstract":[{"text":"An upper bound sieve for rational points on suitable varieties isdeveloped, together with applications tocounting rational points in thin sets,to local solubility in families, and to the notion of “friable” rational pointswith respect to divisors. In the special case of quadrics, sharper estimates areobtained by developing a version of the Selberg sieve for rational points.","lang":"eng"}],"doi":"10.1090/tran/7514","arxiv":1,"day":"15","isi":1,"external_id":{"arxiv":["1705.01999"],"isi":["000464034200019"]},"date_updated":"2023-08-24T14:34:56Z","year":"2019","citation":{"mla":"Browning, Timothy D., and Daniel Loughran. “Sieving Rational Points on Varieties.” <i>Transactions of the American Mathematical Society</i>, vol. 371, no. 8, American Mathematical Society, 2019, pp. 5757–85, doi:<a href=\"https://doi.org/10.1090/tran/7514\">10.1090/tran/7514</a>.","short":"T.D. Browning, D. Loughran, Transactions of the American Mathematical Society 371 (2019) 5757–5785.","ista":"Browning TD, Loughran D. 2019. Sieving rational points on varieties. Transactions of the American Mathematical Society. 371(8), 5757–5785.","ama":"Browning TD, Loughran D. Sieving rational points on varieties. <i>Transactions of the American Mathematical Society</i>. 2019;371(8):5757-5785. doi:<a href=\"https://doi.org/10.1090/tran/7514\">10.1090/tran/7514</a>","apa":"Browning, T. D., &#38; Loughran, D. (2019). Sieving rational points on varieties. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/7514\">https://doi.org/10.1090/tran/7514</a>","chicago":"Browning, Timothy D, and Daniel Loughran. “Sieving Rational Points on Varieties.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2019. <a href=\"https://doi.org/10.1090/tran/7514\">https://doi.org/10.1090/tran/7514</a>.","ieee":"T. D. Browning and D. Loughran, “Sieving rational points on varieties,” <i>Transactions of the American Mathematical Society</i>, vol. 371, no. 8. American Mathematical Society, pp. 5757–5785, 2019."}},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","main_file_link":[{"url":"https://arxiv.org/abs/1709.09476","open_access":"1"}],"oa":1,"publication_identifier":{"issn":["16747283"]},"type":"journal_article","date_published":"2019-12-01T00:00:00Z","language":[{"iso":"eng"}],"month":"12","oa_version":"Preprint","publication":"Science China Mathematics","volume":62,"abstract":[{"lang":"eng","text":"This paper establishes an asymptotic formula with a power-saving error term for the number of rational points of bounded height on the singular cubic surface of ℙ3ℚ given by the following equation 𝑥0(𝑥21+𝑥22)−𝑥33=0 in agreement with the Manin-Peyre conjectures.\r\n"}],"day":"01","arxiv":1,"doi":"10.1007/s11425-018-9543-8","external_id":{"arxiv":["1709.09476"],"isi":["000509102200001"]},"isi":1,"citation":{"short":"R. De La Bretèche, K.N. Destagnol, J. Liu, J. Wu, Y. Zhao, Science China Mathematics 62 (2019) 2435–2446.","mla":"De La Bretèche, Régis, et al. “On a Certain Non-Split Cubic Surface.” <i>Science China Mathematics</i>, vol. 62, no. 12, Springer, 2019, pp. 2435–2446, doi:<a href=\"https://doi.org/10.1007/s11425-018-9543-8\">10.1007/s11425-018-9543-8</a>.","ista":"De La Bretèche R, Destagnol KN, Liu J, Wu J, Zhao Y. 2019. On a certain non-split cubic surface. Science China Mathematics. 62(12), 2435–2446.","apa":"De La Bretèche, R., Destagnol, K. N., Liu, J., Wu, J., &#38; Zhao, Y. (2019). On a certain non-split cubic surface. <i>Science China Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s11425-018-9543-8\">https://doi.org/10.1007/s11425-018-9543-8</a>","ama":"De La Bretèche R, Destagnol KN, Liu J, Wu J, Zhao Y. On a certain non-split cubic surface. <i>Science China Mathematics</i>. 2019;62(12):2435–2446. doi:<a href=\"https://doi.org/10.1007/s11425-018-9543-8\">10.1007/s11425-018-9543-8</a>","ieee":"R. De La Bretèche, K. N. Destagnol, J. Liu, J. Wu, and Y. Zhao, “On a certain non-split cubic surface,” <i>Science China Mathematics</i>, vol. 62, no. 12. Springer, pp. 2435–2446, 2019.","chicago":"De La Bretèche, Régis, Kevin N Destagnol, Jianya Liu, Jie Wu, and Yongqiang Zhao. “On a Certain Non-Split Cubic Surface.” <i>Science China Mathematics</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s11425-018-9543-8\">https://doi.org/10.1007/s11425-018-9543-8</a>."},"year":"2019","date_updated":"2023-08-28T12:32:20Z","article_type":"original","publisher":"Springer","quality_controlled":"1","page":"2435–2446","intvolume":"        62","title":"On a certain non-split cubic surface","article_processing_charge":"No","date_created":"2019-07-07T21:59:25Z","department":[{"_id":"TiBr"}],"publication_status":"published","issue":"12","author":[{"full_name":"De La Bretèche, Régis","last_name":"De La Bretèche","first_name":"Régis"},{"full_name":"Destagnol, Kevin N","first_name":"Kevin N","last_name":"Destagnol","id":"44DDECBC-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Liu, Jianya","first_name":"Jianya","last_name":"Liu"},{"full_name":"Wu, Jie","last_name":"Wu","first_name":"Jie"},{"last_name":"Zhao","first_name":"Yongqiang","full_name":"Zhao, Yongqiang"}],"scopus_import":"1","_id":"6620"},{"publisher":"Elsevier","article_type":"original","quality_controlled":"1","article_processing_charge":"No","date_created":"2019-09-01T22:00:55Z","department":[{"_id":"TiBr"}],"publication_status":"published","intvolume":"       156","title":"Rational points and prime values of polynomials in moderately many variables","scopus_import":"1","_id":"6835","issue":"11","author":[{"id":"44DDECBC-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin N","last_name":"Destagnol","full_name":"Destagnol, Kevin N"},{"full_name":"Sofos, Efthymios","last_name":"Sofos","first_name":"Efthymios"}],"volume":156,"day":"01","doi":"10.1016/j.bulsci.2019.102794","arxiv":1,"abstract":[{"text":"We derive the Hasse principle and weak approximation for fibrations of certain varieties in the spirit of work by Colliot-Thélène–Sansuc and Harpaz–Skorobogatov–Wittenberg. Our varieties are defined through polynomials in many variables and part of our work is devoted to establishing Schinzel's hypothesis for polynomials of this kind. This last part is achieved by using arguments behind Birch's well-known result regarding the Hasse principle for complete intersections with the notable difference that we prove our result in 50% fewer variables than in the classical Birch setting. We also study the problem of square-free values of an integer polynomial with 66.6% fewer variables than in the Birch setting.","lang":"eng"}],"citation":{"chicago":"Destagnol, Kevin N, and Efthymios Sofos. “Rational Points and Prime Values of Polynomials in Moderately Many Variables.” <i>Bulletin Des Sciences Mathematiques</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.bulsci.2019.102794\">https://doi.org/10.1016/j.bulsci.2019.102794</a>.","ieee":"K. N. Destagnol and E. Sofos, “Rational points and prime values of polynomials in moderately many variables,” <i>Bulletin des Sciences Mathematiques</i>, vol. 156, no. 11. Elsevier, 2019.","apa":"Destagnol, K. N., &#38; Sofos, E. (2019). Rational points and prime values of polynomials in moderately many variables. <i>Bulletin Des Sciences Mathematiques</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.bulsci.2019.102794\">https://doi.org/10.1016/j.bulsci.2019.102794</a>","ama":"Destagnol KN, Sofos E. Rational points and prime values of polynomials in moderately many variables. <i>Bulletin des Sciences Mathematiques</i>. 2019;156(11). doi:<a href=\"https://doi.org/10.1016/j.bulsci.2019.102794\">10.1016/j.bulsci.2019.102794</a>","ista":"Destagnol KN, Sofos E. 2019. Rational points and prime values of polynomials in moderately many variables. Bulletin des Sciences Mathematiques. 156(11), 102794.","short":"K.N. Destagnol, E. Sofos, Bulletin Des Sciences Mathematiques 156 (2019).","mla":"Destagnol, Kevin N., and Efthymios Sofos. “Rational Points and Prime Values of Polynomials in Moderately Many Variables.” <i>Bulletin Des Sciences Mathematiques</i>, vol. 156, no. 11, 102794, Elsevier, 2019, doi:<a href=\"https://doi.org/10.1016/j.bulsci.2019.102794\">10.1016/j.bulsci.2019.102794</a>."},"year":"2019","date_updated":"2023-08-29T07:18:02Z","external_id":{"arxiv":["1801.03082"],"isi":["000496342100002"]},"isi":1,"language":[{"iso":"eng"}],"oa_version":"Preprint","article_number":"102794","month":"11","publication":"Bulletin des Sciences Mathematiques","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1801.03082"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["0007-4497"]},"oa":1,"type":"journal_article","date_published":"2019-11-01T00:00:00Z"},{"publication_status":"published","department":[{"_id":"TiBr"}],"date_created":"2019-04-16T09:13:25Z","article_processing_charge":"No","title":"Counting rational points on biquadratic hypersurfaces","intvolume":"       349","_id":"6310","scopus_import":"1","author":[{"last_name":"Browning","first_name":"Timothy D","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"first_name":"L.Q.","last_name":"Hu","full_name":"Hu, L.Q."}],"publisher":"Elsevier","page":"920-940","quality_controlled":"1","file_date_updated":"2020-07-14T12:47:27Z","doi":"10.1016/j.aim.2019.04.031","arxiv":1,"day":"20","abstract":[{"text":"An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariskiopen subset of an arbitrary smooth biquadratic hypersurface in sufficiently many variables. The proof uses the Hardy–Littlewood circle method.","lang":"eng"}],"date_updated":"2023-08-25T10:11:55Z","citation":{"ieee":"T. D. Browning and L. Q. Hu, “Counting rational points on biquadratic hypersurfaces,” <i>Advances in Mathematics</i>, vol. 349. Elsevier, pp. 920–940, 2019.","chicago":"Browning, Timothy D, and L.Q. Hu. “Counting Rational Points on Biquadratic Hypersurfaces.” <i>Advances in Mathematics</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.aim.2019.04.031\">https://doi.org/10.1016/j.aim.2019.04.031</a>.","ama":"Browning TD, Hu LQ. Counting rational points on biquadratic hypersurfaces. <i>Advances in Mathematics</i>. 2019;349:920-940. doi:<a href=\"https://doi.org/10.1016/j.aim.2019.04.031\">10.1016/j.aim.2019.04.031</a>","apa":"Browning, T. D., &#38; Hu, L. Q. (2019). Counting rational points on biquadratic hypersurfaces. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2019.04.031\">https://doi.org/10.1016/j.aim.2019.04.031</a>","ista":"Browning TD, Hu LQ. 2019. Counting rational points on biquadratic hypersurfaces. Advances in Mathematics. 349, 920–940.","short":"T.D. Browning, L.Q. Hu, Advances in Mathematics 349 (2019) 920–940.","mla":"Browning, Timothy D., and L. Q. Hu. “Counting Rational Points on Biquadratic Hypersurfaces.” <i>Advances in Mathematics</i>, vol. 349, Elsevier, 2019, pp. 920–40, doi:<a href=\"https://doi.org/10.1016/j.aim.2019.04.031\">10.1016/j.aim.2019.04.031</a>."},"year":"2019","isi":1,"external_id":{"arxiv":["1810.08426"],"isi":["000468857300025"]},"volume":349,"ddc":["512"],"oa_version":"Submitted Version","month":"06","publication":"Advances in Mathematics","has_accepted_license":"1","language":[{"iso":"eng"}],"publication_identifier":{"issn":["00018708"],"eissn":["10902082"]},"oa":1,"date_published":"2019-06-20T00:00:00Z","type":"journal_article","file":[{"date_created":"2019-04-16T09:12:20Z","file_size":379158,"checksum":"a63594a3a91b4ba6e2a1b78b0720b3d0","date_updated":"2020-07-14T12:47:27Z","content_type":"application/pdf","file_name":"wliqun.pdf","relation":"main_file","access_level":"open_access","file_id":"6311","creator":"tbrownin"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"}]