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arXiv · 2508.05910

General Boyd-Lawton Theorems with Multivariable Limits

Wayne Aitken·Kimberly Ayers·Hanson Smith
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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.

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Wayne Aitken, Kimberly Ayers, Hanson Smith. 2025-08-08. General Boyd-Lawton Theorems with Multivariable Limits. https://arxiv.org/abs/2508.05910

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