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arXiv · 1305.0112

Sums of class numbers and mixed mock modular forms

Kathrin Bringmann·Ben Kane
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Abstract

In this paper, we consider sums of class numbers of the type $\sum_{m\equiv a\pmod{p}} H(4n-m^2)$, 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.

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Kathrin Bringmann, Ben Kane. 2013-11-03. Sums of class numbers and mixed mock modular forms. https://doi.org/10.1017/s0305004118000348

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