On the critical values of Hecke \(L\)-functions for imaginary quadratic fields

DOI10.1007/BF01388657zbMath0558.12005MaRDI QIDQ762551

Ralph Greenberg

Publication date: 1985

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

Full work available at URL: https://eudml.org/doc/143186

zbMATH Keywords

functional equationcomplex multiplicationimaginary quadratic fieldHecke L-functionscritical zeroesfinitely generated Mordell-Weil groupGrössencharactersL-functions of elliptic curves

Mathematics Subject Classification ID

Quadratic extensions (11R11) Elliptic curves over global fields (11G05) Complex multiplication and moduli of abelian varieties (11G15) Zeta functions and (L)-functions of number fields (11R42)

Related Items (9)

L-functions and division towers ⋮ \(p\)-adic \(L\)-functions and the coniveau filtration on Chow groups. With an appendix by Brian Conrad. ⋮ Quantitative non-vanishing of Dirichlet \(L\)-values modulo \(p\) ⋮ Effective moments of Dirichlet \(L\)-functions in Galois orbits ⋮ Geometry of the eigencurve at CM points and trivial zeros of Katz \(p\)-adic \(L\)-functions ⋮ Anticyclotomic main conjectures for CM modular forms ⋮ Denominators of Eisenstein cohomology classes for \(\text{GL}_2\) over imaginary quadratic fields ⋮ \(p^{\infty}\)-Selmer groups and rational points on CM elliptic curves ⋮ On the anticyclotomic Iwasawa theory of CM forms at supersingular primes

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• On Elliptic Curves with Complex Multiplication as Factors of the Jacobians of Modular Function Fields
• On the Birch and Swinnerton-Dyer conjecture
• On the critical values of Hecke L-series

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