Creative telescoping and generating functions of (variants of) multiple zeta values

TL;DR

This paper develops methods to convert generating series of multiple zeta values into hypergeometric series, applies creative telescoping to derive new evaluations, and resolves open questions in the field.

Contribution

It introduces a novel approach combining hypergeometric series conversion and creative telescoping to evaluate multiple zeta values and their variants.

Findings

Derived new explicit evaluations of multiple zeta values.

Reduced generating functions to polynomials in Riemann zeta values.

Resolved previously open questions in multiple zeta value evaluations.

Abstract

We show how to convert the generating series of interpolated multiple zeta values, or multiple $t$ values, with repeating blocks of length 1 into hypergeometric series. Then we invoke creative telescoping on their generating functions, in some known cases for illustration, and in some apparently new cases, reducing them to polynomials in Riemann zeta values. The new evaluations, including $ \zeta^{1/2}(\{\bar2\}^n,3) $, $ \zeta^\star(\{1,3\}^n,1,2) $ and $ t^{1/2}(2,\{1\}^n,2) $, resolve some questions raised elsewhere, and seem to be non-trivial using other methods.