On the square root of special values of certain \(L\)-series

DOI10.1007/BF01243924zbMath0773.11034OpenAlexW2075835335MaRDI QIDQ1191352

Fernando Rodriguez Villegas

Publication date: 27 September 1992

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143953

zbMATH Keywords

elliptic curveTate-Shafarevich groupHecke characters\(L\)-seriessquare root of special valuestheta series at complex multiplication pointsvalues of Jacobi theta functions

Mathematics Subject Classification ID

Elliptic curves (14H52) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Complex multiplication and moduli of abelian varieties (11G15)

Related Items (12)

\(p\)-adic interpolation of square roots of central values of Hecke \(L\)-functions ⋮ On units related to the arithmetic of elliptic curves with complex multiplication ⋮ Nonvanishing of Hecke \(L\)-functions and the Bloch-Kato conjecture ⋮ A subconvexity bound for Hecke L-functions ⋮ Central values of \(L\)-functions of cubic twists ⋮ Central values of Hecke \(L\)-functions of CM number fields ⋮ On the central derivative of Hecke \(L\)-series ⋮ A nonsplit sum of coefficients of modular forms ⋮ A formula for the central value of certain Hecke \(L\)-functions ⋮ On the 2-adic valuations of central \(L\)-values of elliptic curves ⋮ On Hecke's decomposition of the regular differentials on the modular curve of prime level ⋮ Square root formulas for central values of Hecke \(L\)-series. II

Cites Work

• Arithmetic on elliptic curves with complex multiplication. II
• Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication
• Sur les coefficients de Fourier des formes modulaires de poids demi-entier
• Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur
• The non-vanishing of certain Hecke \(L\)-functions at the center of the critical strip
• \(L\)-functions at \(s=1\). IV: First derivatives at \(s=0\)
• Shimura and Shintani correspondences
• On the zeta-function of an abelian variety with complex multiplication
• On the factors of the Jacobian variety of a modular function field
• FINITENESS OF $ E(\mathbf{Q})$ AND $ \textrm{Ø}(E,\mathbf{Q})$ FOR A SUBCLASS OF WEIL CURVES
• On Elliptic Curves with Complex Multiplication as Factors of the Jacobians of Modular Function Fields
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