The $\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913857151172608 |
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| author | Hirose, Minoru Maesaka, Takumi Seki, Shin-ichiro Watanabe, Taiki |
| author_facet | Hirose, Minoru Maesaka, Takumi Seki, Shin-ichiro Watanabe, Taiki |
| contents | We prove that every multiple zeta value is a $\mathbb{Z}$-linear combination of $ζ(k_1,\dots, k_r)$ where $k_i\geq 2$. Our proof also yields an explicit algorithm for such an expansion. The key ingredient is to introduce modified multiple harmonic sums that partially satisfy the relations among multiple zeta values and to determine the structure of the space generated by them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07221 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones Hirose, Minoru Maesaka, Takumi Seki, Shin-ichiro Watanabe, Taiki Number Theory 11M32 We prove that every multiple zeta value is a $\mathbb{Z}$-linear combination of $ζ(k_1,\dots, k_r)$ where $k_i\geq 2$. Our proof also yields an explicit algorithm for such an expansion. The key ingredient is to introduce modified multiple harmonic sums that partially satisfy the relations among multiple zeta values and to determine the structure of the space generated by them. |
| title | The $\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones |
| topic | Number Theory 11M32 |
| url | https://arxiv.org/abs/2505.07221 |