Central values of Hecke \(L\)-functions of CM number fields

DOI10.1215/S0012-7094-99-09817-4zbMath0965.11045OpenAlexW2021233896MaRDI QIDQ1974929

Tonghai Yang, Fernando Rodriguez Villegas

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-99-09817-4

zbMATH Keywords

theta functionscomplex multiplicationnonvanishingHecke \(L\)-functionsCM elliptic curvescentral special valueMordell-Weil rank zero

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Zeta functions and (L)-functions of number fields (11R42)

Related Items (12)

The vanishing order of certain Hecke \(L\)-functions of imaginary quadratic fields ⋮ Fourier-Jacobi periods and the central value of Rankin-Selberg \(L\)-functions ⋮ Non-vanishing of central \(L\)-values of canonical CM elliptic curves with quadratic twists ⋮ Nonvanishing of Hecke \(L\)-functions and the Bloch-Kato conjecture ⋮ A regularized Siegel-Weil formula on \(U(1,1)\) and application to theta lifting from \(U(1)\) to \(U(1,1)\) ⋮ Common zeros of theta functions and central Hecke L-values of CM number fields of degree 4 ⋮ A nonsplit sum of coefficients of modular forms ⋮ Heegner zeros of theta functions ⋮ Nonvanishing of Hecke \(L\)-functions for CM fields and ranks of Abelian varieties ⋮ Effective nonvanishing of canonical Hecke $L$-functions ⋮ ON ASYMPTOTIC VALUES OF CANONICAL QUADRATIC L-FUNCTIONS ⋮ Effective construction of Hilbert modular forms of half-integral weight

Cites Work

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• Theta dichotomy for unitary groups

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