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On Dirichlet Series and Petersson Products for Siegel Modular Forms

Siegfried BöchererFrancesco Ludovico Chiera — 2008

Annales de l’institut Fourier

We prove that the Dirichlet series of Rankin–Selberg type associated with any pair of (not necessarily cuspidal) Siegel modular forms of degree n and weight k n / 2 has meromorphic continuation to . Moreover, we show that the Petersson product of any pair of square–integrable modular forms of weight k n / 2 may be expressed in terms of the residue at s = k of the associated Dirichlet series.

p -adic measures attached to Siegel modular forms

Siegfried BöchererClaus-Günther Schmidt — 2000

Annales de l'institut Fourier

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 of...

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