Integrality of $v$-adic multiple zeta values

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Publication date: 6 January 2020

Abstract: In this article, we prove the integrality of

v

-adic multiple zeta values (MZVs). For any index

m a t h f r a k s i n m a t h b b N^{r}

and finite place

v i n A := m a t h b b F_{q} [h e t a]

, Chang and Mishiba introduced the notion of the

v

-adic MZVs

z e t a_{A} (m a t h f r a k s)_{v}

, which is a function field analogue of Furusho's

p

-adic MZVs. By estimating the

v

-adic valuation of

z e t a_{A} (m a t h f r a k s)_{v}

, we show that

z e t a_{A} (m a t h f r a k 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.

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