Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis

Lewis, John; Zagier, Don

doi:10.1007/s40687-018-0159-8

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Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis

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Zagier, Don
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Lewis, J., & Zagier, D. (2019). Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis. Research in the Mathematical Sciences, 6(1): 4. doi:10.1007/s40687-018-0159-8.

Cite as: https://hdl.handle.net/21.11116/0000-0004-8AC3-4

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.