Sums of Hurwitz class numbers, CM modular forms, and primes of the form $x^2+ny^2$
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916243961806848 |
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| author | Zindulka, Mikuláš |
| author_facet | Zindulka, Mikuláš |
| contents | 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 $x^2+ny^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07565 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sums of Hurwitz class numbers, CM modular forms, and primes of the form $x^2+ny^2$ Zindulka, Mikuláš Number Theory 11E41, 11F11, 11F27, 11F37, 11G05 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 $x^2+ny^2$. |
| title | Sums of Hurwitz class numbers, CM modular forms, and primes of the form $x^2+ny^2$ |
| topic | Number Theory 11E41, 11F11, 11F27, 11F37, 11G05 |
| url | https://arxiv.org/abs/2405.07565 |