Displaying similar documents to “Special values of zeta functions attached to Siegel modular forms”

p -adic measures attached to Siegel modular forms

Siegfried Böcherer, Claus-Günther Schmidt (2000)

Annales de l'institut Fourier

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We study the critical values of the complex standard- L -function attached to a holomorphic Siegel modular form and of the twists of the L -function by Dirichlet characters. Our main object is for a fixed rational prime number p to interpolate p -adically the essentially algebraic critical L -values as the Dirichlet character varies thus providing a systematic control of denominators of critical values by generalized Kummer congruences. In order to organize this information we prove the existence...

A spectral analysis of automorphic distributions and Poisson summation formulas

André Unterberger (2004)

Annales de l’institut Fourier

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Automorphic distributions are distributions on ℝ d , invariant under the linear action of the group S L ( d , ℤ ) . Combs are characterized by the additional requirement of being measures supported in ℤ d : their decomposition into homogeneous components involves the family ( 𝔈 i λ d ) λ ∈ ℝ , 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...