Multitangent functions and symmetric multiple zeta values

TL;DR

This paper establishes a formula linking multitangent functions and symmetric multiple zeta values, proving conjectures and relations that deepen understanding of their algebraic structures.

Contribution

It introduces a formula connecting two variants of multiple zeta values and proves conjectures and relations related to their algebraic structures.

Findings

Proved Bouillot's conjecture on multitangent functions.

Established an analogue of Kawashima's relation for symmetric multiple zeta values.

Connected different variants of multiple zeta values through a new formula.

Abstract

In this paper, we give a formula that connects two variants of multiple zeta values; multitangent functions and symmetric multiple zeta values. As an application of this formula, we give two results. First, we prove Bouillot's conjecture on the structures of the algebra of multitangent functions. Second, we prove an analogue of the linear part of Kawashima's relation for symmetric multiple zeta values.