On a conjecture by Boyd

Abstract

The aim of this note is to prove the Mahler measure identity $m(x+x^{-1}+y+y^{-1}+5)=6m(x+x^{-1}+y+y^{-1}+1)$ which was conjectured by Boyd. The proof is achieved by proving relationships between regulators of both curves.

Cited by in corpus (5)

• On the Mahler measure of $1+X+1/X+Y+1/Y$
• Regulator of modular units and Mahler measures
• Further explorations of Boyd's conjectures and a conductor 21 elliptic curve
• A functional identity for Mahler measures of non-tempered polynomials
• The Mahler measure of exact polynomials in three variables