A note on evaluations of multiple zeta values

TL;DR

This paper provides a concise proof for specific evaluations of multiple zeta values (MZVs), showing they can be expressed as rational multiples of powers of pi squared, simplifying previous complex proofs.

Contribution

It offers a short, simple proof of known MZV evaluations, enhancing understanding and accessibility of these mathematical results.

Findings

MZVs with certain arguments evaluate to rational multiples of pi squared powers

Simplified proof of evaluations by Borman and Bradley

Clarifies the structure of specific MZV evaluations

Abstract

Multiple zeta values (MZVs) with certain repeated arguments or certain sums of cyclically generated MZVs are evaluated as rational multiple of powers of $\pi^2$. In this paper, we give a short and simple proof of the remarkable evaluations of MZVs established by D. Borman and D. M. Bradley.