The areal Mahler measure under a power change of variables

Abstract

The Mahler measure of a multivariable polynomial is given by an integral over the unit torus, while the areal Mahler measure, defined by Pritsker, is given by an integral over the product of unit disks. It is well-known that the classical Mahler measure is invariant under the change of variables $x\mapsto x^r$, where r is an integer, but this is not the case for the areal Mahler measure. In this note we investigate how the areal Mahler measure changes with this transformation and provide some specific examples.