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A spectral analysis of automorphic distributions and Poisson summation formulas

André Unterberger (2004)

Annales de l’institut Fourier

Automorphic distributions are distributions on d , invariant under the linear action of the group S L ( d , ) . Combs are characterized by the additional requirement of being measures supported in d : their decomposition into homogeneous components involves the family ( 𝔈 i λ d ) λ , of Eisenstein distributions, and the coefficients of the decomposition are given as Dirichlet series 𝒟 ( s ) . Functional equations of the usual (Hecke) kind relative to 𝒟 ( s ) turn out to be equivalent to the invariance of the comb under some modification...

CM liftings of supersingular elliptic curves

Ben Kane (2009)

Journal de Théorie des Nombres de Bordeaux

Assuming GRH, we present an algorithm which inputs a prime p and outputs the set of fundamental discriminants D < 0 such that the reduction map modulo a prime above p from elliptic curves with CM by 𝒪 D to supersingular elliptic curves in characteristic p is surjective. In the algorithm we first determine an explicit constant D p so that | D | > D p implies that the map is necessarily surjective and then we compute explicitly the cases | D | < D p .

Fonction zêta d’Epstein et dilogarithme de Bloch-Wigner

Marie José Bertin (2011)

Journal de Théorie des Nombres de Bordeaux

Nous exprimons certaines séries d’Epstein normalisées en s = 2 comme combinaisons linéaires de dilogarithmes de Bloch-Wigner en des nombres algébriques des corps ( Δ ) pour les discriminants Δ associés à la forme quadratique.

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