On the Mahler measure of hyperelliptic families

Abstract

We prove Boyd's "unexpected coincidence" of the Mahler measures for two families of two-variate polynomials defining curves of genus 2. We further equate the same measures to the Mahler measures of polynomials $y^3-y+x^3-x+kxy$ whose zero loci define elliptic curves for $k\ne 0,\pm 3$.

14 pages

References in corpus (3)

• Regulator of modular units and Mahler measures
• Regulators of Siegel units and applications
• On the Mahler measure of a family of genus 2 curves

Cited by in corpus (2)

• On the Mahler measure of a family of genus 2 curves
• Regulator proofs for Boyd's identities on genus 2 curves