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

DOI10.1007/s40687-018-0159-8zbMath1470.11145arXiv1903.09470OpenAlexW2900802586MaRDI QIDQ2319856

Don Zagier, John B. Lewis

Publication date: 20 August 2019

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.09470

zbMATH Keywords

quantum modular formsMaass Eisenstein series

Mathematics Subject Classification ID

Discontinuous groups and automorphic forms (11F99) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Relations with noncommutative geometry (11M55)

Related Items (5)

Quantum modularity of partial theta series with periodic coefficients ⋮ Unnamed Item ⋮ Limit laws for rational continued fractions and value distribution of quantum modular forms ⋮ Eichler integrals of Eisenstein series as \(q\)-brackets of weighted \(t\)-hook functions on partitions ⋮ Quantum Jacobi forms in number theory, topology, and mathematical physics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Eigenfunctions on symmetric spaces with distribution-valued boundary forms
• The Nyman-Beurling equivalent form for the Riemann hypothesis
• Period functions and cotangent sums
• On two problems concerning linear transformations in Hilbert space
• Period Functions for Maass Wave Forms and Cohomology
• The generalized Stieltjes transform and its inverse
• Function Theory Related to the Group PSL2(ℝ)
• Sequences of Enumerative Geometry: Congruences and Asymptotics
• A Reciprocity Formula for a Cotangent Sum
• A CLOSURE PROBLEM RELATED TO THE RIEMANN ZETA-FUNCTION
• Period functions for Maass wave forms. I.

This page was built for publication: Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis