[{"has_accepted_license":"1","publication":"Forum of Mathematics, Pi","project":[{"_id":"bd95085b-d553-11ed-ba76-e55d3349be45","grant_number":"101076777","name":"Randomness and structure in combinatorics"}],"oa_version":"Published Version","article_number":"e21","month":"08","keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Analysis"],"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":"2023-08-24T00:00:00Z","publication_identifier":{"issn":["2050-5086"]},"oa":1,"file":[{"content_type":"application/pdf","file_name":"2023_ForumMathematics_Kwan.pdf","date_updated":"2023-11-07T09:16:23Z","file_size":1218719,"checksum":"54b824098d59073cc87a308d458b0a3e","date_created":"2023-11-07T09:16:23Z","creator":"dernst","file_id":"14500","relation":"main_file","success":1,"access_level":"open_access"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","scopus_import":"1","_id":"14499","author":[{"id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","first_name":"Matthew Alan","last_name":"Kwan","orcid":"0000-0002-4003-7567","full_name":"Kwan, Matthew Alan"},{"full_name":"Sah, Ashwin","last_name":"Sah","first_name":"Ashwin"},{"full_name":"Sauermann, Lisa","last_name":"Sauermann","first_name":"Lisa"},{"full_name":"Sawhney, Mehtaab","last_name":"Sawhney","first_name":"Mehtaab"}],"department":[{"_id":"MaKw"}],"date_created":"2023-11-07T09:02:48Z","article_processing_charge":"Yes","publication_status":"published","intvolume":"        11","title":"Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture","quality_controlled":"1","file_date_updated":"2023-11-07T09:16:23Z","publisher":"Cambridge University Press","article_type":"original","year":"2023","citation":{"ista":"Kwan MA, Sah A, Sauermann L, Sawhney M. 2023. Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. Forum of Mathematics, Pi. 11, e21.","short":"M.A. Kwan, A. Sah, L. Sauermann, M. Sawhney, Forum of Mathematics, Pi 11 (2023).","mla":"Kwan, Matthew Alan, et al. “Anticoncentration in Ramsey Graphs and a Proof of the Erdős–McKay Conjecture.” <i>Forum of Mathematics, Pi</i>, vol. 11, e21, Cambridge University Press, 2023, doi:<a href=\"https://doi.org/10.1017/fmp.2023.17\">10.1017/fmp.2023.17</a>.","chicago":"Kwan, Matthew Alan, Ashwin Sah, Lisa Sauermann, and Mehtaab Sawhney. “Anticoncentration in Ramsey Graphs and a Proof of the Erdős–McKay Conjecture.” <i>Forum of Mathematics, Pi</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/fmp.2023.17\">https://doi.org/10.1017/fmp.2023.17</a>.","ieee":"M. A. Kwan, A. Sah, L. Sauermann, and M. Sawhney, “Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture,” <i>Forum of Mathematics, Pi</i>, vol. 11. Cambridge University Press, 2023.","ama":"Kwan MA, Sah A, Sauermann L, Sawhney M. Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. <i>Forum of Mathematics, Pi</i>. 2023;11. doi:<a href=\"https://doi.org/10.1017/fmp.2023.17\">10.1017/fmp.2023.17</a>","apa":"Kwan, M. A., Sah, A., Sauermann, L., &#38; Sawhney, M. (2023). Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. <i>Forum of Mathematics, Pi</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fmp.2023.17\">https://doi.org/10.1017/fmp.2023.17</a>"},"date_updated":"2023-11-07T09:18:57Z","external_id":{"arxiv":["2208.02874"]},"day":"24","arxiv":1,"doi":"10.1017/fmp.2023.17","abstract":[{"text":"An n-vertex graph is called C-Ramsey if it has no clique or independent set of size Clog2n (i.e., if it has near-optimal Ramsey behavior). In this paper, we study edge statistics in Ramsey graphs, in particular obtaining very precise control of the distribution of the number of edges in a random vertex subset of a C-Ramsey graph. This brings together two ongoing lines of research: the study of ‘random-like’ properties of Ramsey graphs and the study of small-ball probability for low-degree polynomials of independent random variables.\r\n\r\nThe proof proceeds via an ‘additive structure’ dichotomy on the degree sequence and involves a wide range of different tools from Fourier analysis, random matrix theory, the theory of Boolean functions, probabilistic combinatorics and low-rank approximation. In particular, a key ingredient is a new sharpened version of the quadratic Carbery–Wright theorem on small-ball probability for polynomials of Gaussians, which we believe is of independent interest. One of the consequences of our result is the resolution of an old conjecture of Erdős and McKay, for which Erdős reiterated in several of his open problem collections and for which he offered one of his notorious monetary prizes.","lang":"eng"}],"acknowledgement":"Kwan was supported for part of this work by ERC Starting Grant ‘RANDSTRUCT’ No. 101076777. Sah and Sawhney were supported by NSF Graduate Research Fellowship Program DGE-2141064. Sah was supported by the PD Soros Fellowship. Sauermann was supported by NSF Award DMS-2100157, and for part of this work by a Sloan Research Fellowship.","volume":11,"ddc":["510"]},{"publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"oa":1,"date_published":"2022-10-01T00:00:00Z","type":"journal_article","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2103.03906","open_access":"1"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","month":"10","article_number":"2250036","publication":"Random Matrices: Theory and Applications","language":[{"iso":"eng"}],"keyword":["Discrete Mathematics and Combinatorics","Statistics","Probability and Uncertainty","Statistics and Probability","Algebra and Number Theory"],"arxiv":1,"doi":"10.1142/s2010326322500368","day":"01","abstract":[{"text":"We consider a correlated NxN Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one.","lang":"eng"}],"date_updated":"2023-08-03T06:32:22Z","citation":{"mla":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4, 2250036, World Scientific, 2022, doi:<a href=\"https://doi.org/10.1142/s2010326322500368\">10.1142/s2010326322500368</a>.","short":"J. Reker, Random Matrices: Theory and Applications 11 (2022).","ista":"Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 11(4), 2250036.","ama":"Reker J. On the operator norm of a Hermitian random matrix with correlated entries. <i>Random Matrices: Theory and Applications</i>. 2022;11(4). doi:<a href=\"https://doi.org/10.1142/s2010326322500368\">10.1142/s2010326322500368</a>","apa":"Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated entries. <i>Random Matrices: Theory and Applications</i>. World Scientific. <a href=\"https://doi.org/10.1142/s2010326322500368\">https://doi.org/10.1142/s2010326322500368</a>","ieee":"J. Reker, “On the operator norm of a Hermitian random matrix with correlated entries,” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4. World Scientific, 2022.","chicago":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” <i>Random Matrices: Theory and Applications</i>. World Scientific, 2022. <a href=\"https://doi.org/10.1142/s2010326322500368\">https://doi.org/10.1142/s2010326322500368</a>."},"year":"2022","isi":1,"external_id":{"arxiv":["2103.03906"],"isi":["000848873800001"]},"volume":11,"publication_status":"published","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"date_created":"2022-04-08T07:11:12Z","article_processing_charge":"No","title":"On the operator norm of a Hermitian random matrix with correlated entries","intvolume":"        11","_id":"11135","scopus_import":"1","author":[{"full_name":"Reker, Jana","first_name":"Jana","last_name":"Reker","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9"}],"issue":"4","publisher":"World Scientific","article_type":"original","quality_controlled":"1"},{"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"access_level":"open_access","relation":"main_file","success":1,"creator":"dernst","file_id":"12473","file_size":582962,"checksum":"82abaee3d7837f703e499a9ecbb25b7c","date_created":"2023-02-02T07:32:48Z","file_name":"2022_JournalAlgebra_Brown.pdf","content_type":"application/pdf","date_updated":"2023-02-02T07:32:48Z"}],"oa":1,"publication_identifier":{"issn":["0021-8693"]},"type":"journal_article","date_published":"2022-11-01T00:00:00Z","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)"},"keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"month":"11","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"oa_version":"Published Version","has_accepted_license":"1","publication":"Journal of Algebra","ddc":["510"],"volume":609,"acknowledgement":"We thank Catharina Stroppel and Jens Niklas Eberhardt for interesting discussions. The first author acknowledges the support of the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. The second author is supported by the National Science Foundation Award No. 1803059 and the Australian Research Council grant DP170101579.","abstract":[{"lang":"eng","text":"We classify contravariant pairings between standard Whittaker modules and Verma modules over a complex semisimple Lie algebra. These contravariant pairings are useful in extending several classical techniques for category O to the Miličić–Soergel category N . We introduce a class of costandard modules which generalize dual Verma modules, and describe canonical maps from standard to costandard modules in terms of contravariant pairings.\r\nWe show that costandard modules have unique irreducible submodules and share the same composition factors as the corresponding standard Whittaker modules. We show that costandard modules give an algebraic characterization of the global sections of costandard twisted Harish-Chandra sheaves on the associated flag variety, which are defined using holonomic duality of D-modules. We prove that with these costandard modules, blocks of category\r\nN have the structure of highest weight categories and we establish a BGG reciprocity theorem for N ."}],"day":"01","doi":"10.1016/j.jalgebra.2022.06.017","external_id":{"isi":["000861841100004"]},"isi":1,"year":"2022","citation":{"ama":"Brown A, Romanov A. Contravariant pairings between standard Whittaker modules and Verma modules. <i>Journal of Algebra</i>. 2022;609(11):145-179. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">10.1016/j.jalgebra.2022.06.017</a>","apa":"Brown, A., &#38; Romanov, A. (2022). Contravariant pairings between standard Whittaker modules and Verma modules. <i>Journal of Algebra</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">https://doi.org/10.1016/j.jalgebra.2022.06.017</a>","ieee":"A. Brown and A. Romanov, “Contravariant pairings between standard Whittaker modules and Verma modules,” <i>Journal of Algebra</i>, vol. 609, no. 11. Elsevier, pp. 145–179, 2022.","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” <i>Journal of Algebra</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">https://doi.org/10.1016/j.jalgebra.2022.06.017</a>.","mla":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” <i>Journal of Algebra</i>, vol. 609, no. 11, Elsevier, 2022, pp. 145–79, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">10.1016/j.jalgebra.2022.06.017</a>.","short":"A. Brown, A. Romanov, Journal of Algebra 609 (2022) 145–179.","ista":"Brown A, Romanov A. 2022. Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. 609(11), 145–179."},"date_updated":"2023-08-03T11:56:30Z","article_type":"original","publisher":"Elsevier","file_date_updated":"2023-02-02T07:32:48Z","quality_controlled":"1","ec_funded":1,"page":"145-179","intvolume":"       609","title":"Contravariant pairings between standard Whittaker modules and Verma modules","department":[{"_id":"HeEd"}],"article_processing_charge":"Yes (via OA deal)","date_created":"2022-07-08T11:40:07Z","publication_status":"published","issue":"11","author":[{"first_name":"Adam","last_name":"Brown","full_name":"Brown, Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"full_name":"Romanov, Anna","first_name":"Anna","last_name":"Romanov"}],"scopus_import":"1","_id":"11545"},{"article_type":"original","publisher":"Cambridge University Press","file_date_updated":"2022-01-19T09:27:43Z","quality_controlled":"1","ec_funded":1,"intvolume":"        10","title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","date_created":"2022-01-18T16:18:51Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"article_processing_charge":"Yes","publication_status":"published","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","first_name":"Sven Joscha"},{"last_name":"Teufel","first_name":"Stefan","full_name":"Teufel, Stefan"}],"_id":"10643","ddc":["510"],"acknowledgement":"J.H. acknowledges partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tübingen is gratefully acknowledged.","volume":10,"abstract":[{"lang":"eng","text":"We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n"}],"day":"18","arxiv":1,"doi":"10.1017/fms.2021.80","external_id":{"arxiv":["2012.15239"],"isi":["000743615000001"]},"isi":1,"year":"2022","citation":{"short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e4, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2021.80\">10.1017/fms.2021.80</a>.","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.","apa":"Henheik, S. J., &#38; Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.80\">https://doi.org/10.1017/fms.2021.80</a>","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2021.80\">10.1017/fms.2021.80</a>","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2021.80\">https://doi.org/10.1017/fms.2021.80</a>.","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022."},"date_updated":"2023-08-02T13:53:11Z","keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"language":[{"iso":"eng"}],"article_number":"e4","month":"01","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"oa_version":"Published Version","has_accepted_license":"1","publication":"Forum of Mathematics, Sigma","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"file_size":705323,"checksum":"87592a755adcef22ea590a99dc728dd3","date_created":"2022-01-19T09:27:43Z","content_type":"application/pdf","file_name":"2022_ForumMathSigma_Henheik.pdf","date_updated":"2022-01-19T09:27:43Z","relation":"main_file","success":1,"access_level":"open_access","creator":"cchlebak","file_id":"10646"}],"oa":1,"publication_identifier":{"eissn":["2050-5094"]},"type":"journal_article","date_published":"2022-01-18T00:00:00Z","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)"}},{"quality_controlled":"1","file_date_updated":"2022-08-18T08:02:34Z","publisher":"Springer Nature","article_type":"original","_id":"11916","scopus_import":"1","author":[{"last_name":"Wirth","first_name":"Melchior","full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"issue":"3","publication_status":"published","date_created":"2022-08-18T07:22:24Z","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"JaMa"}],"title":"Kac regularity and domination of quadratic forms","intvolume":"         7","acknowledgement":"The author was supported by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG) via RTG 1523/2. The author would like to thank Daniel Lenz for his support and encouragement during the author’s ongoing graduate studies and him as well as Marcel Schmidt for fruitful discussions on domination of quadratic forms. He wants to thank Batu Güneysu and Peter Stollmann for valuable comments on a preliminary version of this article. He would also like to thank the organizers of the conference Analysis and Geometry on Graphs and Manifolds in Potsdam, where the initial motivation of this article was conceived, and the organizers of the intense activity period Metric Measure Spaces and Ricci Curvature at MPIM in Bonn, where this work was finished.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","volume":7,"ddc":["510"],"date_updated":"2023-02-21T10:08:07Z","year":"2022","citation":{"ista":"Wirth M. 2022. Kac regularity and domination of quadratic forms. Advances in Operator Theory. 7(3), 38.","short":"M. Wirth, Advances in Operator Theory 7 (2022).","mla":"Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” <i>Advances in Operator Theory</i>, vol. 7, no. 3, 38, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s43036-022-00199-w\">10.1007/s43036-022-00199-w</a>.","chicago":"Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” <i>Advances in Operator Theory</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s43036-022-00199-w\">https://doi.org/10.1007/s43036-022-00199-w</a>.","ieee":"M. Wirth, “Kac regularity and domination of quadratic forms,” <i>Advances in Operator Theory</i>, vol. 7, no. 3. Springer Nature, 2022.","apa":"Wirth, M. (2022). Kac regularity and domination of quadratic forms. <i>Advances in Operator Theory</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s43036-022-00199-w\">https://doi.org/10.1007/s43036-022-00199-w</a>","ama":"Wirth M. Kac regularity and domination of quadratic forms. <i>Advances in Operator Theory</i>. 2022;7(3). doi:<a href=\"https://doi.org/10.1007/s43036-022-00199-w\">10.1007/s43036-022-00199-w</a>"},"doi":"10.1007/s43036-022-00199-w","day":"01","abstract":[{"lang":"eng","text":"A domain is called Kac regular for a quadratic form on L2 if every functions vanishing almost everywhere outside the domain can be approximated in form norm by functions with compact support in the domain. It is shown that this notion is stable under domination of quadratic forms. As applications measure perturbations of quasi-regular Dirichlet forms, Cheeger energies on metric measure spaces and Schrödinger operators on manifolds are studied. Along the way a characterization of the Sobolev space with Dirichlet boundary conditions on domains in infinitesimally Riemannian metric measure spaces is obtained."}],"language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory","Analysis"],"publication":"Advances in Operator Theory","has_accepted_license":"1","oa_version":"Published Version","month":"07","article_number":"38","file":[{"date_updated":"2022-08-18T08:02:34Z","file_name":"2022_AdvancesOperatorTheory_Wirth.pdf","content_type":"application/pdf","date_created":"2022-08-18T08:02:34Z","checksum":"913474844a1b38264fb710746d5e2e98","file_size":389060,"file_id":"11921","creator":"dernst","relation":"main_file","access_level":"open_access","success":1}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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)"},"date_published":"2022-07-01T00:00:00Z","type":"journal_article","publication_identifier":{"eissn":["2538-225X"]},"oa":1},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","file":[{"date_updated":"2023-01-24T10:02:40Z","file_name":"2022_ForumMath_Cipolloni.pdf","content_type":"application/pdf","date_created":"2023-01-24T10:02:40Z","file_size":817089,"checksum":"94a049aeb1eea5497aa097712a73c400","file_id":"12356","creator":"dernst","relation":"main_file","success":1,"access_level":"open_access"}],"oa":1,"publication_identifier":{"issn":["2050-5094"]},"date_published":"2022-10-27T00:00:00Z","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)"},"language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"month":"10","article_number":"e96","oa_version":"Published Version","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publication":"Forum of Mathematics, Sigma","has_accepted_license":"1","ddc":["510"],"volume":10,"acknowledgement":"L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331. D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","abstract":[{"text":"We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables.","lang":"eng"}],"doi":"10.1017/fms.2022.86","day":"27","isi":1,"external_id":{"isi":["000873719200001"]},"date_updated":"2023-08-04T09:00:35Z","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96.","mla":"Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e96, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>"},"year":"2022","article_type":"original","publisher":"Cambridge University Press","file_date_updated":"2023-01-24T10:02:40Z","quality_controlled":"1","ec_funded":1,"title":"Rank-uniform local law for Wigner matrices","intvolume":"        10","publication_status":"published","date_created":"2023-01-12T12:07:30Z","department":[{"_id":"LaEr"}],"article_processing_charge":"No","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"_id":"12148","scopus_import":"1"},{"volume":654,"acknowledgement":"Work partially supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337.","ddc":["510"],"doi":"10.1016/j.laa.2022.09.001","day":"01","abstract":[{"lang":"eng","text":"Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The latter says that quantum operations can never increase the relative entropy. The monotonicity versions often have many advantages, and often have direct physical application, as in the example just mentioned. Moreover, the monotonicity results are often valid for a larger class of maps than, say, quantum operations (which are completely positive). In this paper we prove several new monotonicity results, the first of which is a monotonicity theorem that has as a simple corollary a celebrated concavity theorem of Epstein. Our starting points are the monotonicity versions of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs of these in their general forms using interpolation. We then prove our new monotonicity theorems by several duality arguments."}],"date_updated":"2023-08-04T09:24:51Z","year":"2022","citation":{"ama":"Carlen EA, Zhang H. Monotonicity versions of Epstein’s concavity theorem and related inequalities. <i>Linear Algebra and its Applications</i>. 2022;654:289-310. doi:<a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">10.1016/j.laa.2022.09.001</a>","apa":"Carlen, E. A., &#38; Zhang, H. (2022). Monotonicity versions of Epstein’s concavity theorem and related inequalities. <i>Linear Algebra and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">https://doi.org/10.1016/j.laa.2022.09.001</a>","chicago":"Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” <i>Linear Algebra and Its Applications</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">https://doi.org/10.1016/j.laa.2022.09.001</a>.","ieee":"E. A. Carlen and H. Zhang, “Monotonicity versions of Epstein’s concavity theorem and related inequalities,” <i>Linear Algebra and its Applications</i>, vol. 654. Elsevier, pp. 289–310, 2022.","short":"E.A. Carlen, H. Zhang, Linear Algebra and Its Applications 654 (2022) 289–310.","mla":"Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” <i>Linear Algebra and Its Applications</i>, vol. 654, Elsevier, 2022, pp. 289–310, doi:<a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">10.1016/j.laa.2022.09.001</a>.","ista":"Carlen EA, Zhang H. 2022. Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and its Applications. 654, 289–310."},"isi":1,"external_id":{"isi":["000860689600014"]},"publisher":"Elsevier","article_type":"original","page":"289-310","quality_controlled":"1","file_date_updated":"2023-01-27T08:08:39Z","publication_status":"published","date_created":"2023-01-16T09:46:38Z","department":[{"_id":"JaMa"}],"article_processing_charge":"Yes (via OA deal)","title":"Monotonicity versions of Epstein's concavity theorem and related inequalities","intvolume":"       654","_id":"12216","scopus_import":"1","author":[{"full_name":"Carlen, Eric A.","first_name":"Eric A.","last_name":"Carlen"},{"full_name":"Zhang, Haonan","last_name":"Zhang","first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425"}],"file":[{"file_name":"2022_LinearAlgebra_Carlen.pdf","content_type":"application/pdf","date_updated":"2023-01-27T08:08:39Z","file_size":441184,"checksum":"cf3cb7e7e34baa967849f01d8f0c1ae4","date_created":"2023-01-27T08:08:39Z","creator":"dernst","file_id":"12415","access_level":"open_access","success":1,"relation":"main_file"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["0024-3795"]},"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)"},"date_published":"2022-12-01T00:00:00Z","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Numerical Analysis","Algebra and Number Theory"],"oa_version":"Published Version","project":[{"grant_number":"M03337","name":"Curvature-dimension in noncommutative analysis","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6"}],"month":"12","publication":"Linear Algebra and its Applications","has_accepted_license":"1"},{"main_file_link":[{"url":"https://arxiv.org/abs/1909.03266","open_access":"1"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","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","acknowledgement":"We would like to thank the anonymous referees for carefully reading the paper and for their remarks and suggestions.","volume":157,"arxiv":1,"doi":"10.1112/s0010437x21007351","day":"28","abstract":[{"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.","lang":"eng"}],"date_updated":"2023-08-17T06:59:16Z","citation":{"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>.","short":"P. Autissier, D. Bonolis, Y. Lamzouri, Compositio Mathematica 157 (2021) 1610–1651.","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.","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>","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>","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.","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>."},"year":"2021","isi":1,"external_id":{"arxiv":["1909.03266"],"isi":["000667289300001"]},"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","last_name":"Autissier","first_name":"Pascal"},{"id":"6A459894-5FDD-11E9-AF35-BB24E6697425","first_name":"Dante","last_name":"Bonolis","full_name":"Bonolis, Dante"},{"full_name":"Lamzouri, Youness","first_name":"Youness","last_name":"Lamzouri"}],"issue":"7"},{"publisher":"Springer Nature","article_type":"original","quality_controlled":"1","date_created":"2023-01-16T11:44:39Z","article_processing_charge":"No","publication_status":"published","intvolume":"         7","title":"Primitive divisors of sequences associated to elliptic curves with complex multiplication","scopus_import":"1","_id":"12308","issue":"2","author":[{"full_name":"Verzobio, Matteo","orcid":"0000-0002-0854-0306","last_name":"Verzobio","first_name":"Matteo","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb"}],"volume":7,"extern":"1","day":"20","doi":"10.1007/s40993-021-00267-9","abstract":[{"text":"Let P and Q be two points on an elliptic curve defined over a number field K. For α∈End(E), define Bα to be the OK-integral ideal generated by the denominator of x(α(P)+Q). Let O be a subring of End(E), that is a Dedekind domain. We will study the sequence {Bα}α∈O. We will show that, for all but finitely many α∈O, the ideal Bα has a primitive divisor when P is a non-torsion point and there exist two endomorphisms g≠0 and f so that f(P)=g(Q). This is a generalization of previous results on elliptic divisibility sequences.","lang":"eng"}],"year":"2021","citation":{"mla":"Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves with Complex Multiplication.” <i>Research in Number Theory</i>, vol. 7, no. 2, 37, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s40993-021-00267-9\">10.1007/s40993-021-00267-9</a>.","short":"M. Verzobio, Research in Number Theory 7 (2021).","ista":"Verzobio M. 2021. Primitive divisors of sequences associated to elliptic curves with complex multiplication. Research in Number Theory. 7(2), 37.","ama":"Verzobio M. Primitive divisors of sequences associated to elliptic curves with complex multiplication. <i>Research in Number Theory</i>. 2021;7(2). doi:<a href=\"https://doi.org/10.1007/s40993-021-00267-9\">10.1007/s40993-021-00267-9</a>","apa":"Verzobio, M. (2021). Primitive divisors of sequences associated to elliptic curves with complex multiplication. <i>Research in Number Theory</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40993-021-00267-9\">https://doi.org/10.1007/s40993-021-00267-9</a>","chicago":"Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves with Complex Multiplication.” <i>Research in Number Theory</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s40993-021-00267-9\">https://doi.org/10.1007/s40993-021-00267-9</a>.","ieee":"M. Verzobio, “Primitive divisors of sequences associated to elliptic curves with complex multiplication,” <i>Research in Number Theory</i>, vol. 7, no. 2. Springer Nature, 2021."},"date_updated":"2023-05-08T12:00:17Z","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"oa_version":"Published Version","article_number":"37","month":"05","publication":"Research in Number Theory","main_file_link":[{"url":"https://doi.org/10.1007/s40993-021-00267-9","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","publication_identifier":{"issn":["2522-0160","2363-9555"]},"oa":1,"type":"journal_article","date_published":"2021-05-20T00:00:00Z"},{"extern":"1","volume":198,"external_id":{"arxiv":["2001.09634"]},"year":"2021","citation":{"ista":"Verzobio M. 2021. Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. Acta Arithmetica. 198(2), 129–168.","short":"M. Verzobio, Acta Arithmetica 198 (2021) 129–168.","mla":"Verzobio, Matteo. “Primitive Divisors of Elliptic Divisibility Sequences for Elliptic Curves with J=1728.” <i>Acta Arithmetica</i>, vol. 198, no. 2, Institute of Mathematics, Polish Academy of Sciences, 2021, pp. 129–68, doi:<a href=\"https://doi.org/10.4064/aa191016-30-7\">10.4064/aa191016-30-7</a>.","ieee":"M. Verzobio, “Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728,” <i>Acta Arithmetica</i>, vol. 198, no. 2. Institute of Mathematics, Polish Academy of Sciences, pp. 129–168, 2021.","chicago":"Verzobio, Matteo. “Primitive Divisors of Elliptic Divisibility Sequences for Elliptic Curves with J=1728.” <i>Acta Arithmetica</i>. Institute of Mathematics, Polish Academy of Sciences, 2021. <a href=\"https://doi.org/10.4064/aa191016-30-7\">https://doi.org/10.4064/aa191016-30-7</a>.","apa":"Verzobio, M. (2021). Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. <i>Acta Arithmetica</i>. Institute of Mathematics, Polish Academy of Sciences. <a href=\"https://doi.org/10.4064/aa191016-30-7\">https://doi.org/10.4064/aa191016-30-7</a>","ama":"Verzobio M. Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. <i>Acta Arithmetica</i>. 2021;198(2):129-168. doi:<a href=\"https://doi.org/10.4064/aa191016-30-7\">10.4064/aa191016-30-7</a>"},"date_updated":"2023-05-08T11:58:14Z","abstract":[{"text":"Take a rational elliptic curve defined by the equation y2=x3+ax in minimal form and consider the sequence Bn of the denominators of the abscissas of the iterate of a non-torsion point. We show that B5m has a primitive divisor for every m. Then, we show how to generalize this method to the terms of the form Bmp with p a prime congruent to 1 modulo 4.","lang":"eng"}],"day":"04","doi":"10.4064/aa191016-30-7","arxiv":1,"quality_controlled":"1","page":"129-168","article_type":"original","publisher":"Institute of Mathematics, Polish Academy of Sciences","issue":"2","author":[{"id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","orcid":"0000-0002-0854-0306","full_name":"Verzobio, Matteo","first_name":"Matteo","last_name":"Verzobio"}],"scopus_import":"1","_id":"12309","intvolume":"       198","title":"Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728","article_processing_charge":"No","date_created":"2023-01-16T11:44:54Z","publication_status":"published","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2001.09634"}],"type":"journal_article","date_published":"2021-01-04T00:00:00Z","oa":1,"publication_identifier":{"issn":["0065-1036","1730-6264"]},"keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"publication":"Acta Arithmetica","month":"01","oa_version":"Preprint"},{"author":[{"full_name":"Verzobio, Matteo","orcid":"0000-0002-0854-0306","last_name":"Verzobio","first_name":"Matteo","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb"}],"issue":"4","_id":"12310","scopus_import":"1","title":"Primitive divisors of sequences associated to elliptic curves","intvolume":"       209","publication_status":"published","article_processing_charge":"No","date_created":"2023-01-16T11:45:07Z","page":"378-390","quality_controlled":"1","article_type":"original","publisher":"Elsevier","external_id":{"arxiv":["1906.00632"]},"date_updated":"2023-05-10T11:14:56Z","year":"2020","citation":{"chicago":"Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves.” <i>Journal of Number Theory</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.jnt.2019.09.003\">https://doi.org/10.1016/j.jnt.2019.09.003</a>.","ieee":"M. Verzobio, “Primitive divisors of sequences associated to elliptic curves,” <i>Journal of Number Theory</i>, vol. 209, no. 4. Elsevier, pp. 378–390, 2020.","apa":"Verzobio, M. (2020). Primitive divisors of sequences associated to elliptic curves. <i>Journal of Number Theory</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jnt.2019.09.003\">https://doi.org/10.1016/j.jnt.2019.09.003</a>","ama":"Verzobio M. Primitive divisors of sequences associated to elliptic curves. <i>Journal of Number Theory</i>. 2020;209(4):378-390. doi:<a href=\"https://doi.org/10.1016/j.jnt.2019.09.003\">10.1016/j.jnt.2019.09.003</a>","ista":"Verzobio M. 2020. Primitive divisors of sequences associated to elliptic curves. Journal of Number Theory. 209(4), 378–390.","mla":"Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves.” <i>Journal of Number Theory</i>, vol. 209, no. 4, Elsevier, 2020, pp. 378–90, doi:<a href=\"https://doi.org/10.1016/j.jnt.2019.09.003\">10.1016/j.jnt.2019.09.003</a>.","short":"M. Verzobio, Journal of Number Theory 209 (2020) 378–390."},"abstract":[{"lang":"eng","text":"Let  be a sequence of points on an elliptic curve defined over a number field K. In this paper, we study the denominators of the x-coordinates of this sequence. We prove that, if Q is a torsion point of prime order, then for n large enough there always exists a primitive divisor. Later on, we show the link between the study of the primitive divisors and a Lang-Trotter conjecture. Indeed, given two points P and Q on the elliptic curve, we prove a lower bound for the number of primes p such that P is in the orbit of Q modulo p."}],"arxiv":1,"doi":"10.1016/j.jnt.2019.09.003","day":"01","extern":"1","volume":209,"publication":"Journal of Number Theory","month":"04","oa_version":"Preprint","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"date_published":"2020-04-01T00:00:00Z","type":"journal_article","oa":1,"publication_identifier":{"issn":["0022-314X"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1906.00632"}]},{"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,"external_id":{"arxiv":["1807.08986"]},"citation":{"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.","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>.","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>","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>","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.","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>.","short":"S. Ionica, P. Kılıçer, K. Lauter, E. Lorenzo García, M.-A. Manzateanu, M. Massierer, C. Vincent, Research in Number Theory 5 (2019)."},"year":"2019","date_updated":"2023-09-05T15:39:31Z","abstract":[{"lang":"eng","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."}],"day":"02","doi":"10.1007/s40993-018-0146-6","arxiv":1,"quality_controlled":"1","article_type":"original","publisher":"Springer Nature","author":[{"full_name":"Ionica, Sorina","last_name":"Ionica","first_name":"Sorina"},{"first_name":"Pınar","last_name":"Kılıçer","full_name":"Kılıçer, Pınar"},{"first_name":"Kristin","last_name":"Lauter","full_name":"Lauter, Kristin"},{"first_name":"Elisa","last_name":"Lorenzo García","full_name":"Lorenzo García, Elisa"},{"id":"be8d652e-a908-11ec-82a4-e2867729459c","first_name":"Maria-Adelina","last_name":"Manzateanu","full_name":"Manzateanu, Maria-Adelina"},{"first_name":"Maike","last_name":"Massierer","full_name":"Massierer, Maike"},{"full_name":"Vincent, Christelle","last_name":"Vincent","first_name":"Christelle"}],"scopus_import":"1","_id":"10874","intvolume":"         5","title":"Modular invariants for genus 3 hyperelliptic curves","department":[{"_id":"TiBr"}],"article_processing_charge":"No","date_created":"2022-03-18T12:09:48Z","publication_status":"published","status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","main_file_link":[{"url":"https://arxiv.org/abs/1807.08986","open_access":"1"}],"type":"journal_article","date_published":"2019-01-02T00:00:00Z","oa":1,"publication_identifier":{"issn":["2522-0160"],"eissn":["2363-9555"]},"keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"publication":"Research in Number Theory","article_number":"9","month":"01","oa_version":"Preprint"}]