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Mathematische Zeitschrift

, Volume 283, Issue 3–4, pp 1185–1193 | Cite as

On the Mahler measure of a family of genus 2 curves

  • Marie José Bertin
  • Wadim Zudilin
Article

Abstract

We establish a general identity between the Mahler measures \(\mathrm {m}(Q_k(x,y))\) and \(\mathrm {m}(P_k(x,y))\) of two polynomial families, where \(Q_k(x,y)=0\) and \(P_k(x,y)=0\) are generically hyperelliptic and elliptic curves, respectively.

Keywords

Mahler measure L-value Elliptic curve Hyperelliptic curve Elliptic integral 

Mathematics Subject Classification

Primary 11F67 Secondary 11F11 11F20 11G16 11G55 11R06 14H52 19F27 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institut de MathématiquesUniversité Pierre et Marie Curie (Paris 6)ParisFrance
  2. 2.School of Mathematical and Physical SciencesThe University of NewcastleCallaghanAustralia

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