A Novel Summation Formula for the Hurwitz-Kronecker Class Number
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912580467949568 |
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| author | Tsai, Yi-Ju |
| author_facet | Tsai, Yi-Ju |
| contents | The purpose of this paper is to present a novel and elegant summation formula for $H_w$, the Kronecker-Hurwitz class number. Specifically, for any prime $p$, we have the formula: $$ \sum_{t^2<p} H_w(t^2-p) = \frac{p-2}{3}. $$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08281 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Novel Summation Formula for the Hurwitz-Kronecker Class Number Tsai, Yi-Ju Number Theory The purpose of this paper is to present a novel and elegant summation formula for $H_w$, the Kronecker-Hurwitz class number. Specifically, for any prime $p$, we have the formula: $$ \sum_{t^2<p} H_w(t^2-p) = \frac{p-2}{3}. $$ |
| title | A Novel Summation Formula for the Hurwitz-Kronecker Class Number |
| topic | Number Theory |
| url | https://arxiv.org/abs/2509.08281 |