Mahler measures of a family of non-tempered polynomials and Boyd's conjectures

Abstract

We prove an identity relating Mahler measures of a certain family of non-tempered polynomials to those of tempered polynomials. Evaluations of Mahler measures of some polynomials in the first family are also given in terms of special values of $L$-functions and logarithms. Finally, we prove Boyd's conjectures for conductor $30$ elliptic curves using our new identity, Brunault-Mellit-Zudilin's formula and additional functional identities for Mahler measures.

21 pages

References in corpus (6)

• From $L$-series of elliptic curves to Mahler measures
• Regulator of modular units and Mahler measures
• Regulators of Siegel units and applications
• On the Mahler measure of a family of genus 2 curves
• Further explorations of Boyd's conjectures and a conductor 21 elliptic curve
• Parametrizing elliptic curves by modular units

Cited by in corpus (2)

• Mahler measure of a non-reciprocal family of elliptic curves
• A functional identity for Mahler measures of non-tempered polynomials