Sums of Hurwitz Class Numbers and newform of weight 2 and level 49
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915034005766144 |
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| author | Guo, Fangmin |
| author_facet | Guo, Fangmin |
| contents | 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 $p=x^2+7y^2$ $(p\equiv 1,2,4 \mod 7)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16894 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sums of Hurwitz Class Numbers and newform of weight 2 and level 49 Guo, Fangmin Number Theory 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 $p=x^2+7y^2$ $(p\equiv 1,2,4 \mod 7)$. |
| title | Sums of Hurwitz Class Numbers and newform of weight 2 and level 49 |
| topic | Number Theory |
| url | https://arxiv.org/abs/2411.16894 |