Structural properties of multiple zeta values

TL;DR

This paper explores the properties of multiple zeta values, extending classical identities to zeta functions based on zeros of arbitrary functions, and introduces a complementary zeta function related to quasisymmetric functions.

Contribution

It generalizes classical multiple zeta value identities to a broader class of zeta functions and introduces the complementary zeta function concept.

Findings

Classical identities hold for zeta functions built on zeros of any function.

Introduction of the complementary zeta function linked to quasisymmetric functions.

Extension of multiple zeta value theory to more general settings.

Abstract

We study some classical identities for multiple zeta values and show that they still hold for zeta functions built on the zeros of an arbitrary function. We introduce the complementary zeta function of a system, which naturally occurs when lifting identities for multiple zeta values to identities for quasisymmetric functions.