Regulator of modular units and Mahler measures

Abstract

We present a proof of the formula, due to Mellit and Brunault, which evaluates an integral of the regulator of two modular units to the value of the $L$-series of a modular form of weight 2 at $s=2$. Applications of the formula to computing Mahler measures are discussed.

15 pages

Cited by in corpus (14)

• Regulators of Siegel units and applications
• Mahler measures as linear combinations of $L$-values of multiple modular forms
• On the Mahler measure of a family of genus 2 curves
• Further explorations of Boyd's conjectures and a conductor 21 elliptic curve
• On the Mahler measure of hyperelliptic families
• Parametrizing elliptic curves by modular units
• Régulateurs modulaires explicites via la méthode de Rogers-Zudilin
• Mahler measures of a family of non-tempered polynomials and Boyd's conjectures
• Regulator proofs for Boyd's identities on genus 2 curves
• Mahler's measure and elliptic curves with potential complex multiplication
• A functional identity for Mahler measures of non-tempered polynomials
• Mahler measure of a non-reciprocal family of elliptic curves
• The Mahler measure of exact polynomials in three variables
• $L$-values for conductor $32$