A sum-shuffle formula for zeta values in Tate algebras

TL;DR

This paper establishes a sum-shuffle formula for multiple zeta values within Tate algebras over positive characteristic fields, demonstrating their algebraic structure and relations.

Contribution

It introduces a sum-shuffle formula for multiple zeta values in Tate algebras and shows these values form an algebra over finite fields.

Findings

Sum-shuffle formula for multiple zeta values in Tate algebras

The algebra generated by these zeta values is closed under addition and multiplication

Implication that these values form an _p-algebra

Abstract

We prove a sum-shuffle formula for multiple zeta values in Tate algebras (in positive characteristic), introduced in \cite{PEL3}.This follows from an analog result for double twisted power sums, implying that an ${\mathbb{F}\_p$-vector space generated by multiple zeta values in Tate algebras is an ${\mathbb{F}\_p$-algebra.