General Boyd-Lawton Theorems with Multivariable Limits
Number Theory
2025-08-11 v1
Abstract
The classical Boyd-Lawton theorem concerning Mahler measures has recently been extended to multivariable limits by Brunault, Guilloux, Mehrabdollahei, and Pengo. In another direction, the single-variable Boyd-Lawton theorem has been generalized to various extensions of Mahler measure by Issa and Lal\'in. The goal of this paper is to present a cohesive framework for extending single-variable Boyd-Lawton theorems to multivariable Boyd-Lawton theorems. With this, we broaden the single-variable Boyd-Lawton theorems of Issa and Lal\'in to multivariable versions in the direction of Brunault, Guilloux, Mehrabdollahei, and Pengo, providing a generalization of both works.
Cite
@article{arxiv.2508.05910,
title = {General Boyd-Lawton Theorems with Multivariable Limits},
author = {Wayne Aitken and Kimberly Ayers and Hanson Smith},
journal= {arXiv preprint arXiv:2508.05910},
year = {2025}
}