Quaternionic Mahler measure
Number Theory
2024-03-06 v1 Complex Variables
Abstract
We introduce the quaternionic Mahler measure for non-commutative polynomials, extending the classical complex Mahler measure. We establish the existence of quaternionic Mahler measure for slice regular polynomials in one and two variables. We study the quaternionic Mahler measure for real and slice regular polynomials, and consider the associated Lehmer problem. Various formulas of quaternionic Mahler measures are proved.
Keywords
Cite
@article{arxiv.2403.02851,
title = {Quaternionic Mahler measure},
author = {Weijia Wang and Hao Zhang},
journal= {arXiv preprint arXiv:2403.02851},
year = {2024}
}