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 s ∈ N r and finite place v ∈ A := Fq[θ], Chang and Mishiba introduced the notion of the v-adic MZVs ζA(s)v, which is a function field analogue of Furusho's p-adic MZVs. By estimating the v-adic valuation of ζA(s)v, we show that ζA(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.