论文标题
$ v $ - adic多重Zeta值的完整性
Integrality of $v$-adic multiple zeta values
论文作者
论文摘要
在本文中，我们证明了$ v $ -ADIC多重Zeta值（MZVS）的完整性。对于任何索引$ \ Mathfrak {s} \ in \ Mathbb {n}^r $和有限的位置$ v \ in a：= = \ Mathbb {f} _q [θ] $，Chang和Mishiba介绍了$ V $ -V $ -ADIC MZVS $ QUIND的概念Furusho的$ P $ -ADIC MZVS。通过估计$ v $ -ADIC估值的$ζ_A（\ Mathfrak {s}）_ V $，我们表明$ζ_A（\ Mathfrak {s}）_ V $是几乎所有$ v $的$ V $ -ADIC INTEGER。该结果可以看作是$ p $ -ADIC MZVS完整性的功能字段类似物，Akagi-Hirose-Yasuda和Chatzistamatiou证明了这一点。
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.
