Integrality of $v$-adic multiple zeta values

Abstract

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 $v\in A:={\mathbb{F}}_q[\theta ]$, Chang and Mishiba introduced the notion of the $v$-adic MZVs ${\zeta }_A(\mathfrak{s}{)}_v$, which is a function field analogue of Furusho's $p$-adic MZVs. By estimating the $v$-adic valuation of ${\zeta }_A(\mathfrak{s}{)}_v$, we show that ${\zeta }_A(\mathfrak{s}{)}_v$ 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.

22 pages

References in corpus (3)

• p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation
• Linear independence of monomials of multizeta values in positive characteristic
• Multizeta values for F_q[t], their period interpretation and relations between them

Cited by in corpus (1)

• Linear relations among algebraic points on tensor powers of the Carlitz module