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arXiv · 2411.16894

Sums of Hurwitz Class Numbers and newform of weight 2 and level 49

Fangmin Guo
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Abstract

We consider sums of Hurwitz class number $H_{m,M}(n)=\sum_{t\equiv m (\text{mod} M)}{H(4n-t^2)}$, where $H(N)$ denotes the Hurwitz class number. In this article, we consider the case of $M=7$. By completing the mixed mock modular form generated by $H_{m,7}(n)$, We obtain the formula of modular forms consist of a computable part and a part from newform 49.2.a.a whose prime terms of Fourier expansion has a connection with with $p=x^2+7y^2$ $(p\equiv 1,2,4 \mod 7)$.

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Fangmin Guo. 2024-11-25. Sums of Hurwitz Class Numbers and newform of weight 2 and level 49. https://arxiv.org/abs/2411.16894

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