An invariant property of Mahler measure

TL;DR

This paper introduces a variable transformation that preserves Mahler measure, enabling the construction of complex polynomials with specific measures and confirming several conjectural formulas in the field.

Contribution

It presents a novel change of variables technique that maintains Mahler measure and applies it to verify conjectures by Boyd and Brunault.

Findings

Constructed polynomials with prescribed Mahler measures.

Confirmed conjectural numerical formulas related to Mahler measure.

Provided a new method for analyzing Mahler measure invariance.

Abstract

We exhibit a change of variables that maintains the Mahler measure of a given polynomial. This method leads to the construction of highly non-trivial polynomials with given Mahler measure and settles some conjectural numerical formulas due to Boyd and Brunault.