Mahler measure and the WZ algorithm

TL;DR

This paper employs the Wilf-Zeilberger method to prove identities involving Mahler measures, providing new proofs and connecting them to elliptic dilogarithms, thereby addressing a challenge posed by Kontsevich and Zagier.

Contribution

It introduces a novel application of the WZ algorithm to Mahler measures and translates identities into elliptic dilogarithm formulas, advancing the understanding of periods.

Findings

New proof of Lalín's Mahler measure formula

Translation of identities into elliptic dilogarithm expressions

Resolution of a challenge problem by Kontsevich and Zagier

Abstract

We use the Wilf-Zeilberger method to prove identities between Mahler measures of polynomials. In particular, we offer a new proof of a formula due to Lal\'{i}n, and we show how to translate the identity into a formula involving elliptic dilogarithms. This work settles a challenge problem proposed by Kontsevich and Zagier in their paper "Periods".