Interpolation of multiple zeta and zeta-star values

TL;DR

This paper introduces polynomial interpolations connecting multiple zeta and zeta-star values, applying these to the two-one conjecture and establishing a cyclic sum formula.

Contribution

It defines new polynomial interpolations for multiple zeta values, providing novel tools for conjecture analysis and proving a cyclic sum formula.

Findings

Polynomial interpolation between multiple zeta and zeta-star values.

Application to the two-one conjecture of Ohno-Zudilin.

Proof of the cyclic sum formula for the interpolating polynomials.

Abstract

We define polynomials of one variable t whose values at t=0 and 1 are the multiple zeta values and the multiple zeta-star values, respectively. We give an application to the two-one conjecture of Ohno-Zudilin, and also prove the cyclic sum formula for these polynomials.