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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.01836 |
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| _version_ | 1866913923100311552 |
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| author | Kriz, Daniel Nordentoft, Asbjørn Christian |
| author_facet | Kriz, Daniel Nordentoft, Asbjørn Christian |
| contents | We obtain a formula for the $p$-adic valuation of weighted moments of central $L$-values of holomorphic cusp forms twisted by Dirichlet characters of order $p$. In some cases we give an arithmetic interpretation of the constants in the formula. The result is obtained via the study of the digit map, turning a horizontal $p$-adic measure into a vertical one, applied to the horizontal $p$-adic $L$-functions as defined by the authors in previous work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01836 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $p$-adic moments of $L$-functions Kriz, Daniel Nordentoft, Asbjørn Christian Number Theory 11F67 We obtain a formula for the $p$-adic valuation of weighted moments of central $L$-values of holomorphic cusp forms twisted by Dirichlet characters of order $p$. In some cases we give an arithmetic interpretation of the constants in the formula. The result is obtained via the study of the digit map, turning a horizontal $p$-adic measure into a vertical one, applied to the horizontal $p$-adic $L$-functions as defined by the authors in previous work. |
| title | $p$-adic moments of $L$-functions |
| topic | Number Theory 11F67 |
| url | https://arxiv.org/abs/2507.01836 |