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| Format: | Preprint |
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2020
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| Online Access: | https://arxiv.org/abs/2001.01855 |
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| _version_ | 1866911691021746176 |
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| author | Chen, Yen-Tsung |
| author_facet | Chen, Yen-Tsung |
| contents | In this article, we prove the integrality of $v$-adic multiple zeta values (MZVs). For any index $\mathfrak{s}\in\mathbb{N}^r$ and finite place $v\in A:=\mathbb{F}_q[θ]$, Chang and Mishiba introduced the notion of the $v$-adic MZVs $ζ_A(\mathfrak{s})_v$, which is a function field analogue of Furusho's $p$-adic MZVs. By estimating the $v$-adic valuation of $ζ_A(\mathfrak{s})_v$, we show that $ζ_A(\mathfrak{s})_v$ is a $v$-adic integer for almost all $v$. This result can be viewed as a function field analogue of the integrality of $p$-adic MZVs, which was proved by Akagi-Hirose-Yasuda and Chatzistamatiou. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_01855 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Integrality of $v$-adic multiple zeta values Chen, Yen-Tsung Number Theory In this article, we prove the integrality of $v$-adic multiple zeta values (MZVs). For any index $\mathfrak{s}\in\mathbb{N}^r$ and finite place $v\in A:=\mathbb{F}_q[θ]$, Chang and Mishiba introduced the notion of the $v$-adic MZVs $ζ_A(\mathfrak{s})_v$, which is a function field analogue of Furusho's $p$-adic MZVs. By estimating the $v$-adic valuation of $ζ_A(\mathfrak{s})_v$, we show that $ζ_A(\mathfrak{s})_v$ is a $v$-adic integer for almost all $v$. This result can be viewed as a function field analogue of the integrality of $p$-adic MZVs, which was proved by Akagi-Hirose-Yasuda and Chatzistamatiou. |
| title | Integrality of $v$-adic multiple zeta values |
| topic | Number Theory |
| url | https://arxiv.org/abs/2001.01855 |