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Functional equations for Mahler measures of genus-one curves

Matilde N. Lalín·Mathew D. Rogers
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Abstract

In this paper we will establish functional equations for Mahler measures of families of genus-one two-variable polynomials. These families were previously studied by Beauville, and their Mahler measures were considered by Boyd, Rodriguez-Villegas, Bertin, Zagier, and Stienstra. Our functional equations allow us to prove identities between Mahler measures that were conjectured by Boyd. As a corollary, we also establish some new transformations for hypergeometric functions.

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BibTeXRIS

Matilde N. Lalín, Mathew D. Rogers. 2007-02-09. Functional equations for Mahler measures of genus-one curves. https://arxiv.org/abs/math/0612007

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