A cyclic analogue of multiple zeta values

TL;DR

This paper introduces a cyclic analogue of multiple zeta values, establishing identities and relations that extend known formulas and provide new insights into their algebraic structure.

Contribution

It defines a cyclic analogue of multiple zeta values, proves an integral-series identity, and constructs new linear relations generalizing existing formulas.

Findings

Proved an integral=series identity for CMZVs

Constructed new $Q$-linear relations among CMZVs

Extended the cyclic sum formula to CMZVs

Abstract

We consider a cyclic analogue of multiple zeta values (CMZVs), which has two kinds of expressions; series and integral expression. We prove an `integral$=$series' type identity for CMZVs. By using this identity, we construct two classes of $\mathbb{Q}$-linear relations among CMZVs. One of them is a generalization of the cyclic sum formula for multiple zeta-star values. We also give an alternative proof of the derivation relation for multiple zeta values.