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arXiv · 2405.07565

Sums of Hurwitz class numbers, CM modular forms, and primes of the form $x^2+ny^2$

Mikuláš Zindulka
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Abstract

We consider sums of Hurwitz class numbers of the type $\sum_{t \equiv m \pmod{M}}H(4p-t^2)$, where $M$ is composite. For $M=6$ and $8$, we show that these sums can be expressed in terms of coefficients of CM cusp forms. This leads to explicit formulas which depend on the expression of $p$ in the form $x^2+ny^2$.

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Mikuláš Zindulka. 2024-05-13. Sums of Hurwitz class numbers, CM modular forms, and primes of the form $x^2+ny^2$. https://arxiv.org/abs/2405.07565

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