Regulators of Siegel units and applications

Abstract

We present a formula for the regulator of two arbitrary Siegel units in terms of L-values of pairwise products of Eisenstein series of weight one. We give applications to Boyd's conjectures and Zagier's conjectures for elliptic curves of conductor 14, 21, 35, 48 and 54.

19 pages

References in corpus (2)

• Regulator of modular units and Mahler measures
• Parametrizing elliptic curves by modular units

Cited by in corpus (10)

• On the Mahler measure of hyperelliptic families
• Further explorations of Boyd's conjectures and a conductor 21 elliptic curve
• Mahler measures of a family of non-tempered polynomials and Boyd's conjectures
• Mahler measures of elliptic modular surfaces
• Régulateurs modulaires explicites via la méthode de Rogers-Zudilin
• Mahler measure of a non-reciprocal family of elliptic curves
• On the $K_4$ group of modular curves
• A functional identity for Mahler measures of non-tempered polynomials
• Mahler's measure and elliptic curves with potential complex multiplication
• $L$-values for conductor $32$