Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis
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40687_2018_Article_159.pdf
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2.09 MB
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Adobe PDF
Checksum (MD5)
9f24c8326c1f9814a25969442ba9b86c
Author(s)
Zagier, Don
Lewis, John B
Date Issued
November 2018
Journal
Research in the Mathematical Sciences
Publisher
Springer International Publishing
Citation
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
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s40687-018-0159-8
