Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis
Number Theory
2019-03-25 v1
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.
Keywords
Cite
@article{arxiv.1903.09470,
title = {Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis},
author = {John Lewis and Don Zagier},
journal= {arXiv preprint arXiv:1903.09470},
year = {2019}
}
Comments
24 pages, 8 figures