Summation formulas for Hurwitz class numbers and other mock modular coefficients
Number Theory
2025-05-12 v1
Abstract
We prove a formula for weighted sums of the first coefficients of mock modular forms of moderate growth and apply it to Hurwitz class numbers and coefficients of negative half integral weight Eisenstein series, which take the form of certain quadratic Dirichlet -values. Our formula is a mock modular version of a Bessel-sum identity proved by Chandrasekharan and Narasimhan for Dirichlet series satisfying a functional equation. Our proof utilizes -functions for mock modular Eisenstein series defined by Shankadhar and Singh.
Cite
@article{arxiv.2505.05574,
title = {Summation formulas for Hurwitz class numbers and other mock modular coefficients},
author = {Olivia Beckwith and Nikolaos Diamantis and Rajat Gupta and Larry Rolen and Kalani Thalagoda},
journal= {arXiv preprint arXiv:2505.05574},
year = {2025}
}