On the Mahler measure of (1+x)(1+y)+z

2023/05/04 by François Brunault, Brunault, François · 1 citation
Mathematics · #11G16 #11R06 #19E15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #K-Theory and Homology (math.KT) #Meromorphic and Entire Functions #Number Theory (math.NT) #Primary 19F27 #Secondary 11F67

paper · pdf · doi:10.48550/arxiv.2305.02992

openalex publication_date 2023/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a conjecture of Boyd and Rodriguez Villegas relating the Mahler measure of the polynomial (1+x)(1+y)+z and the value at s=3 of the L-function of an elliptic curve of conductor 15. The proof makes use of the computation by Zudilin and the author of the regulator of certain K₄ classes on modular curves.

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

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