An explicit Galois descent for multiple $t$-values of maximal height

TL;DR

This paper provides an explicit Galois descent formula linking maximal height multiple t-values to classical multiple zeta values, utilizing iterated beta integrals, and applies it to evaluate multiple zeta-half values.

Contribution

It introduces a new explicit formula for Galois descent of multiple t-values of maximal height, connecting them to classical multiple zeta values.

Findings

Derived an explicit Galois descent formula for multiple t-values.

Connected multiple t-values of maximal height to classical multiple zeta values.

Applied the formula to evaluate multiple zeta-half values.

Abstract

We give an explicit formula for the Galois descent expressing multiple $t$-values of maximal height in terms of classical multiple zeta values, making precise Murakami's earlier motivic result. Our results rely on the theory of iterated beta integrals. We apply this formula to obtain evaluations of various multiple zeta-half values.