A family of integrals related to values of the Riemann zeta function
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917824456294400 |
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| author | Kumar, Rahul Levrie, Paul Pain, Jean-Christophe Scharaschkin, Victor |
| author_facet | Kumar, Rahul Levrie, Paul Pain, Jean-Christophe Scharaschkin, Victor |
| contents | We propose a relation between values of the Riemann zeta function $ζ$ and a family of integrals. This results in an integral representation for $ζ(2p)$, where $p$ is a positive integer, and an expression of $ζ(2p+1)$ involving one of the above mentioned integrals together with a harmonic-number sum. Simplification of the latter eventually leads to an integral representation of $ζ(2p + 1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06546 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A family of integrals related to values of the Riemann zeta function Kumar, Rahul Levrie, Paul Pain, Jean-Christophe Scharaschkin, Victor Number Theory We propose a relation between values of the Riemann zeta function $ζ$ and a family of integrals. This results in an integral representation for $ζ(2p)$, where $p$ is a positive integer, and an expression of $ζ(2p+1)$ involving one of the above mentioned integrals together with a harmonic-number sum. Simplification of the latter eventually leads to an integral representation of $ζ(2p + 1)$. |
| title | A family of integrals related to values of the Riemann zeta function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2409.06546 |