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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.20509 |
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| _version_ | 1866911971504291840 |
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| author | Ihara, Kentaro Nakamura, Yayoi Yamamoto, Shuji |
| author_facet | Ihara, Kentaro Nakamura, Yayoi Yamamoto, Shuji |
| contents | We introduce an analytic function $Ψ(s_1,\ldots,s_r;w)$ that interpolates truncated multiple zeta functions $ζ_N(s_1,\ldots,s_r)$. We represent this interpolant as a Mellin transform of a function $G(q_1,\ldots,q_r;w)$ and, using this expression, give the analytic continuation. Further, the harmonic product relations for $Ψ$ and $G$ are established via relevant Hopf algebra structures, and some properties of the function $G$ are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20509 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interpolant of truncated multiple zeta functions Ihara, Kentaro Nakamura, Yayoi Yamamoto, Shuji Number Theory We introduce an analytic function $Ψ(s_1,\ldots,s_r;w)$ that interpolates truncated multiple zeta functions $ζ_N(s_1,\ldots,s_r)$. We represent this interpolant as a Mellin transform of a function $G(q_1,\ldots,q_r;w)$ and, using this expression, give the analytic continuation. Further, the harmonic product relations for $Ψ$ and $G$ are established via relevant Hopf algebra structures, and some properties of the function $G$ are provided. |
| title | Interpolant of truncated multiple zeta functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2407.20509 |