Intersection of duality and derivation relations for multiple zeta values

TL;DR

This paper explores the relationship between duality and derivation relations in multiple zeta values, providing an explicit characterization of their intersection and advancing understanding of their algebraic structure.

Contribution

It offers a precise description of how duality and derivation relations intersect within the framework of multiple zeta values, clarifying their algebraic connections.

Findings

Explicit characterization of the intersection of duality and derivation relations

Derivation relation as a specialization of the extended double shuffle relation

Enhanced understanding of the algebraic structure of multiple zeta values

Abstract

The duality relation is a basic family of linear relations for multiple zeta values. The extended double shuffle relation (EDSR) is one of the families of relations expected to generate all linear relations among multiple zeta values, but it remains unclear as to whether all duality relations can be deduced from the EDSR. In the present paper, regarding the family generated by the duality relation and the family generated by the derivation relation, an explicit characterization of their intersection is obtained. Here, the derivation relation is a specialization of the EDSR.