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

2019/03/22 by John B. Lewis, Don Zagier, Lewis, John +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1903.09470

openalex publication_date 2019/03/22 · openalex created_date 2019/10/10 · openalex updated_date 2026/07/28

Abstract

We show that an asymptotic property of the determinants of certain matrices\nwhose entries are finite sums of cotangents with rational arguments is\nequivalent to the GRH for odd Dirichlet characters. This is then connected to\nthe existence of certain quantum modular forms related to Maass Eisenstein\nseries.\n

Citations

• On two problems concerning linear transformations in hilbert space

Cited by

• On twisted period functions and Moments of a weighted mean square of Dirichlet L-functions on the critical line

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