On the Mahler measure of a family of genus 2 curves

Abstract

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

9 pages

References in corpus (2)

• Regulator of modular units and Mahler measures
• On the Mahler measure of hyperelliptic families

Cited by in corpus (4)

• On the Mahler measure of hyperelliptic families
• Mahler measures of a family of non-tempered polynomials and Boyd's conjectures
• Regulator proofs for Boyd's identities on genus 2 curves
• A functional identity for Mahler measures of non-tempered polynomials