Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis
Download40687_2018_Article_159.pdf (2.090Mb)
PUBLISHER_CC
Publisher with Creative Commons License
Creative Commons Attribution
Terms of use
Metadata
Show full item recordAbstract
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.
Date issued
2018-11Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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.
Version: Final published version
ISSN
2522-0144
2197-9847