Summation formulas for Hurwitz class numbers and other mock modular coefficients

2025/05/08 by Olivia Beckwith, Nikolaos Diamantis, Beckwith, Olivia +7 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2505.05574

openalex publication_date 2025/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a formula for weighted sums of the first n 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 L-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 L-functions for mock modular Eisenstein series defined by Shankadhar and Singh.

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