Kummer's criterion for the special values of Hecke L-functions of imaginary quadratic fields and congruences among cusp forms

DOI10.1007/BF01389222zbMath0485.10019MaRDI QIDQ1164085

Haruzo Hida

Publication date: 1982

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

Full work available at URL: https://eudml.org/doc/142891

zbMATH Keywords

congruencesGalois extensionzeta functionprimitive formirregular primescongruence divisorsgeneralization of Kummer criterionprimitive cusp formspecial values of Hecke L-functions

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11)

Related Items

Unnamed Item, Galois representations into \(\text{GL}_2(\mathbb Z_pX)\) attached to ordinary cusp forms., Modular forms in characteristic \(\ell\) and special values of their \(L\)-functions, A deformation problem for Galois representations over imaginary quadratic fields, Generalized Bernoulli numbers and congruence of modular forms, Iwasawa modules attached to congruences of cusp forms, An \(R = T\) theorem for imaginary quadratic fields, Unnamed Item, Geometry of the eigencurve at CM points and trivial zeros of Katz \(p\)-adic \(L\)-functions, Un sous-groupe $p$-divisible de la jacobienne de $X_1(N p_r)$ comme module sur l'algèbre de Hecke, Constancy of adjoint \(\mathcal L\)-invariant, Unnamed Item, On the Eisenstein ideal for imaginary quadratic fields, Elliptic units and a Kummer's criterion for imaginary quadratic fields, Arithmetic properties of the Shimura-Shintani-Waldspurger correspondence. With an appendix by Brian Conrad., A geometric view on Iwasawa theory, Mod p Hecke operators and congruences between modular forms

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