The Mahler measure of x + 1/x + y + 1/y + 4 ± 42 and Beilinson’s conjecture

DOI10.1142/s1793042124500088WikidataQ123269810 ScholiaQ123269810MaRDI QIDQ6186048

Hang Liu, Hourong Qin, Qingzhong Ji, Xue Jun Guo

Publication date: 9 January 2024

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

zbMATH Keywords

elliptic curve\(L\)-functionMahler measureBeilinson's conjecture

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Étale cohomology, higher regulators, zeta and (L)-functions ((K)-theoretic aspects) (19F27)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Eta-quotients and theta functions
• Sur les représentations galoisiennes modulo \(\ell\) attachées aux formes modulaires. (On Galois representations modulo \(\ell\) attached to modular forms)
• On the modularity level of modular abelian varieties over number fields
• Functional equations for Mahler measures of genus-one
• Higher regulators and values of \(L\)-functions
• Automorphic forms on \(O_{s+2,2}(\mathbb R)\) and infinite products
• OnK₂of Certain Families of Curves
• 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
• On $L$-functions of quadratic $\mathbb {Q}$-curves
• Abelian varieties over Q and modular forms
• Mahler Measures as Linear Combinations ofL–values of Multiple Modular Forms
• A functional identity for Mahler measures of non-tempered polynomials
• Many Variations of Mahler Measures
• The Mahler measure of a Weierstrass form
• Weber's class invariants
• On the arithmetic of abelian varieties

This page was built for publication: The Mahler measure of x + 1/x + y + 1/y + 4 ± 42 and Beilinson’s conjecture