The Mahler measure of a genus 3 family

DOI10.1007/s11139-019-00241-1zbMath1468.11222OpenAlexW3034795274MaRDI QIDQ829655

Matilde N. Lalín, Gang Wu

Publication date: 6 May 2021

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-019-00241-1

zbMATH Keywords

elliptic curvesMahler measurespecial values of \(L\)-functionselliptic regulatorgenus 3 curves

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Étale cohomology, higher regulators, zeta and (L)-functions ((K)-theoretic aspects) (19F27) Elliptic functions and integrals (33E05)

Related Items (2)

Mahler Measure of Families of Polynomials Defining Genus 2 and 3 Curves ⋮ A shifted Mahler measure identity for Boyd’s family

Uses Software

• GitHub

Cites Work

• On the Mahler measure of a family of genus 2 curves
• Higher regulators and values of L-functions of curves
• Factorization of certain cyclotomic functions
• Elliptic dilogarithms and parallel lines
• On the Mahler measure of hyperelliptic families
• On Measures of Polynomials in Several Variables: Corrigendum
• Speculations Concerning the Range of Mahler's Measure
• 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
• Higher Regulators, Algebraic 𝐾-Theory, and Zeta Functions of Elliptic Curves
• Regulator proofs for Boyd’s identities on genus 2 curves
• FromL-series of elliptic curves to Mahler measures
• Regulator of modular units and Mahler measures
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