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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...

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