General Boyd-Lawton Theorems with Multivariable Limits

TL;DR

This paper develops a unified framework to extend Boyd-Lawton theorems from single-variable to multivariable Mahler measures, integrating recent advances and broadening their applicability.

Contribution

It introduces a cohesive approach to generalize single-variable Boyd-Lawton theorems to multivariable cases, combining previous extensions by Issa, Lalín, and others.

Findings

Unified multivariable Boyd-Lawton theorems framework

Extension of Issa and Lalín's results to multivariable setting

Broadened applicability of Mahler measure limits

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.