Weighted sum formulas of multiple zeta values with even arguments

TL;DR

This paper derives weighted sum formulas for multiple zeta values at even arguments and their zeta-star analogues, confirming conjectures by Guo, Lei, and Zhao, with coefficients expressed as symmetric polynomials.

Contribution

It provides the first proof of conjectured weighted sum formulas for multiple zeta values at even arguments and their zeta-star counterparts.

Findings

Weighted sum formulas for zeta values at even arguments derived.

Weighted sum formulas for multiple zeta values and zeta-star analogues established.

Conjectures by Guo, Lei, and Zhao confirmed.

Abstract

We obtain a weighted sum formula of the zeta values at even arguments, and a weighted sum formula of the multiple zeta values with even arguments and its zeta-star analogue. The weight coefficients are given by (symmetric) polynomials of the arguments. These weighted sum formulas for the zeta values and for the multiple zeta values were conjectured by L. Guo, P. Lei and J. Zhao.