Regulators of Siegel units and applications

DOI10.1016/J.JNT.2015.12.019zbMath1344.19001arXiv1504.08127OpenAlexW2963511811MaRDI QIDQ5964556

François Brunault

Publication date: 29 February 2016

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.08127

zbMATH Keywords

elliptic curves\(L\)-functionsBoyd's conjecturesMahler measuresmodular unitsregulatorsZagier's conjectures

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11) Étale cohomology, higher regulators, zeta and (L)-functions ((K)-theoretic aspects) (19F27) Elliptic and modular units (11G16)

Related Items (11)

On the Mahler measure of hyperelliptic families ⋮ The Mahler measure of a Weierstrass form ⋮ A shifted Mahler measure identity for Boyd’s family ⋮ Identities of Mahler measures of certain polynomials defining curves of arbitrary genus ⋮ Mahler's measure for polynomials in several variables ⋮ Mahler measures of a family of non-tempered polynomials and Boyd's conjectures ⋮ Mahler measures of elliptic modular surfaces ⋮ Elliptic dilogarithms and parallel lines ⋮ A functional identity for Mahler measures of non-tempered polynomials ⋮ \(L\)-values for conductor 32 ⋮ Régulateurs modulaires explicites via la méthode de Rogers–Zudilin

Uses Software

• Magma
• ecdata

Cites Work

• On Zagier's conjecture for base changes of elliptic curves
• The Magma algebra system. I: The user language
• Toric modular forms and nonvanishing of L-functions
• PARAMETRIZING ELLIPTIC CURVES BY MODULAR UNITS
• Mahler's Measure and Special Values of L-functions
• Deligne periods of mixed motives, $K$-theory and the entropy of certain $\mathbb {Z}^n$-actions
• FromL-series of elliptic curves to Mahler measures
• Regulator of modular units and Mahler measures
• Modular Forms
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Regulators of Siegel units and applications