Reciprocity For Dedekind Sums via Conical Zeta Values
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915692745326592 |
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| author | Torres-Nova, Yerko |
| author_facet | Torres-Nova, Yerko |
| contents | We study reciprocity formulas for Dedekind sums associated with absolutely continuous functions, extending the classical Dedekind-Rademacher reciprocity formula. In particular, we treat the case of periodic Bernoulli functions. Our approach generalizes an integral method and uses Fourier analysis to show that the reciprocity for polynomial-type functions admits a geometric interpretation in terms of conical zeta values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20542 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reciprocity For Dedekind Sums via Conical Zeta Values Torres-Nova, Yerko Number Theory 11F20, 11B68, 11M32 We study reciprocity formulas for Dedekind sums associated with absolutely continuous functions, extending the classical Dedekind-Rademacher reciprocity formula. In particular, we treat the case of periodic Bernoulli functions. Our approach generalizes an integral method and uses Fourier analysis to show that the reciprocity for polynomial-type functions admits a geometric interpretation in terms of conical zeta values. |
| title | Reciprocity For Dedekind Sums via Conical Zeta Values |
| topic | Number Theory 11F20, 11B68, 11M32 |
| url | https://arxiv.org/abs/2512.20542 |