On triple zeta values of even weight and their connections with period polynomials

TL;DR

This paper explores the relationships between triple zeta values of even weight and period polynomials, providing bounds on the dimension of related vector spaces and deepening understanding of their mathematical structure.

Contribution

It introduces new connections between triple zeta values and period polynomials, and establishes an upper bound on the dimension of their span.

Findings

Connected triple zeta values with period polynomials

Derived an upper bound on the dimension of the span of certain triple zeta values

Enhanced understanding of the structure of triple zeta values of even weight

Abstract

We study triple zeta values of even weight and show various connections with period polynomials. As a result, an (expected) upper bound of the dimension of the vector space spanned by certain triple zeta values is obtained.