Generating functions for sums of polynomial multiple zeta values

TL;DR

This paper introduces generating functions for polynomial multiple zeta values, revealing their connection to sum formulas and symmetric variants, and unifies these concepts through identities involving Schur multiple zeta values.

Contribution

It provides a new generating function approach that generalizes sum formulas for multiple zeta values and their symmetric counterparts, linking them via Schur multiple zeta values.

Findings

Derived sum formulas for polynomial multiple zeta(-star) values

Unified sum formulas for multiple zeta and symmetric multiple zeta values

Established identities involving Schur multiple zeta values

Abstract

The sum formulas for multiple zeta(-star) values and symmetric multiple zeta(-star) values bear a striking resemblance. We explain the resemblance in a rather straightforward manner using an identity that involves the Schur multiple zeta values. We also obtain the sum formula for polynomial multiple zeta(-star) values in terms of generating functions, simultaneously generalizing the sum formulas for multiple zeta(-star) values and symmetric multiple zeta(-star) values.