Multiple zeta-star values and multiple integrals

TL;DR

This paper introduces a new class of multiple integrals linked to combinatorial data that unify various multiple zeta and zeta-star values, providing transparent relations among them.

Contribution

It develops integral expressions for multiple harmonic sums and zeta-star values, and introduces 2-labeled posets to unify different types of multiple zeta values.

Findings

Integral expressions for finite multiple harmonic sums and zeta-star values.

A new class of multiple integrals associated with 2-labeled posets.

Transparent derivation of relations among various multiple zeta values.

Abstract

We prove a kind of integral expressions for finite multiple harmonic sums and multiple zeta-star values. Moreover, we introduce a class of multiple integrals, associated with some combinatorial data (called 2-labeled posets). This class includes both multiple zeta and zeta-star values of Euler-Zagier type, and also several other types of multiple zeta values. We show that these integrals can be used to obtain some relations among such zeta values quite transparently.