Limits of Mahler measures in multiple variables
Abstract
We prove that certain sequences of Laurent polynomials, obtained from a fixed Laurent polynomial P by monomial substitutions, give rise to sequences of Mahler measures which converge to the Mahler measure of P. This generalizes previous work of Boyd and Lawton, who considered univariate monomial substitutions. We provide moreover an explicit upper bound for the error term in this convergence, generalizing work of Dimitrov and Habegger, and a full asymptotic expansion for a family of 2-variable polynomials, whose Mahler measures were studied independently by the third author.
Cite
@article{arxiv.2203.12259,
title = {Limits of Mahler measures in multiple variables},
author = {François Brunault and Antonin Guilloux and Mahya Mehrabdollahei and Riccardo Pengo},
journal= {arXiv preprint arXiv:2203.12259},
year = {2025}
}
Comments
In V2, the error term has been improved with respect to V1, with a new bound of independant interest given in Theorem 4.6. This bound replaces a reference to Dimitrov-Habegger in the previous version, and follows closely their method