2021/09/29 by Berend Ringeling, Wadim Zudilin, Ringeling, Berend +1
Computer Science · Mathematics · #33C75 #33E05 #Algebraic Geometry and Number Theory #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #K-Theory and Homology (math.KT) #Number Theory (math.NT) #Polynomial and algebraic computation #Primary 11R06 #Secondary 11G05
paper · pdf · doi:10.48550/arxiv.2109.14380
openalex publication_date 2021/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, Hang Liu and Hourong Qin came up with a numerical observation about the relation between the Mahler measures of one hyperelliptic and two elliptic families. The discoverers foresee a proof of the identities "by extending ideas in" two papers of Matilde Lal'ın and Gang Wu, the ideas based on a theorem of Spencer Bloch and explicit diamond-operation calculations on the underlying curves. We prove the relation using the already available diamond-free methodology. While finding such relations for the Mahler measures remains an art, proving them afterwards is mere complex (analysis) exercising.