Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis
We show that an asymptotic property of the determinants of certain matrices whose entries are finite sums of cotangents with rational arguments is equivalent to the GRH for odd Dirichlet characters. This is then connected to the existence of certain quantum modular forms related to Maass Eisenstein...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer International Publishing
2018
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| Online Access: | http://hdl.handle.net/1721.1/119799 https://orcid.org/0000-0002-3822-6131 |
| _version_ | 1826191737758941184 |
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| author | Zagier, Don Lewis, John B |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Zagier, Don Lewis, John B |
| author_sort | Zagier, Don |
| collection | MIT |
| description | We show that an asymptotic property of the determinants of certain matrices whose entries are finite sums of cotangents with rational arguments is equivalent to the GRH for odd Dirichlet characters. This is then connected to the existence of certain quantum modular forms related to Maass Eisenstein series. |
| first_indexed | 2024-09-23T09:00:50Z |
| format | Article |
| id | mit-1721.1/119799 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:00:50Z |
| publishDate | 2018 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1197992024-06-27T14:43:28Z Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis Zagier, Don Lewis, John B Massachusetts Institute of Technology. Department of Mathematics Lewis, John B We show that an asymptotic property of the determinants of certain matrices whose entries are finite sums of cotangents with rational arguments is equivalent to the GRH for odd Dirichlet characters. This is then connected to the existence of certain quantum modular forms related to Maass Eisenstein series. 2018-12-20T18:26:12Z 2018-12-20T18:26:12Z 2018-11 2018-05 2018-12-07T04:44:53Z Article http://purl.org/eprint/type/JournalArticle 2522-0144 2197-9847 http://hdl.handle.net/1721.1/119799 Lewis, John, and Don Zagier. “Cotangent Sums, Quantum Modular Forms, and the Generalized Riemann Hypothesis.” Research in the Mathematical Sciences, vol. 6, no. 1, Mar. 2019. © 2018 The Authors https://orcid.org/0000-0002-3822-6131 en https://doi.org/10.1007/s40687-018-0159-8 Research in the Mathematical Sciences Creative Commons Attribution http://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer International Publishing Springer International Publishing |
| spellingShingle | Zagier, Don Lewis, John B Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis |
| title | Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis |
| title_full | Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis |
| title_fullStr | Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis |
| title_full_unstemmed | Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis |
| title_short | Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis |
| title_sort | cotangent sums quantum modular forms and the generalized riemann hypothesis |
| url | http://hdl.handle.net/1721.1/119799 https://orcid.org/0000-0002-3822-6131 |
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