Sums of class numbers and mixed mock modular forms

Abstract

In this paper, we consider sums of class numbers of the type ${\sum }_{m\equiv a(\mathrm{mod}p)}H(4n-m^2)$, where $p$ is an odd prime, $n\in \mathbb{N},$ and $a\in \mathbb{Z}$. By showing that these are coefficients of mixed mock modular forms, we obtain explicit formulas. Using these formulas for $p=5$ and $7$, we then prove a conjecture of Brown et al. in the case that $n=\ell$ is prime.

References in corpus (2)

• Mock Theta Functions
• Elliptic curves, modular forms, and sums of Hurwitz class numbers

Cited by in corpus (5)

• Eichler-Selberg Type Identities for Mixed Mock Modular Forms
• Vector-valued Hirzebruch-Zagier series and class number sums
• Theta lifts for Lorentzian lattices and coefficients of mock theta functions
• Optimal estimates for an average of Hurwitz class numbers
• Mock Modular Forms and Class Number Relations