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Equations for Mahler measure and isogenies

Matilde N. Lalín — 2013

Journal de Théorie des Nombres de Bordeaux

We study some functional equations between Mahler measures of genus-one curves in terms of isogenies between the curves. These equations have the potential to establish relationships between Mahler measure and especial values of $L$ -functions. These notes are based on a talk that the author gave at the “Cuartas Jornadas de Teoría de Números”, Bilbao, 2011.

Higher Mahler measure of an n-variable family

Matilde N. Lalín; Jean-Sébastien Lechasseur — 2016

Acta Arithmetica

We prove formulas for the k-higher Mahler measure of a family of rational functions with an arbitrary number of variables. Our formulas reveal relations with multiple polylogarithms evaluated at certain roots of unity.

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