Evaluations of the areal Mahler measure of multivariable polynomials

2023/06/27 by Matilde Laĺın, Lalin, Matilde N., Subham Roy +1 · 2 citations
Mathematics · #11R06 (Primary) 11M06 #11R42 #30C10 (Secondary) #Analytic and geometric function theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2306.15727

openalex publication_date 2023/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We exhibit some nontrivial evaluations of the areal Mahler measure of multivariable polynomials, defined by Pritsker [Pri08] by considering the integral over the product of unit disks instead of the unit torus as in the standard case. As in the case of the classical Mahler measure, we find examples yielding special values of L-functions.

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• Areal Weil Heights
• Integral Representations and Asymptotics for a Family of Areal Mahler Measures

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