Displaying similar documents to “Congruences for Siegel modular forms”

Class invariants and cyclotomic unit groups from special values of modular units

Amanda Folsom (2008)

Journal de Théorie des Nombres de Bordeaux

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In this article we obtain class invariants and cyclotomic unit groups by considering specializations of modular units. We construct these modular units from functional solutions to higher order q -recurrence equations given by Selberg in his work generalizing the Rogers-Ramanujan identities. As a corollary, we provide a new proof of a result of Zagier and Gupta, originally considered by Gauss, regarding the Gauss periods. These results comprise part of the author’s 2006 Ph.D. thesis []...

On Dirichlet Series and Petersson Products for Siegel Modular Forms

Siegfried Böcherer, Francesco Ludovico Chiera (2008)

Annales de l’institut Fourier

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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 ℂ . 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.

Congruences between modular forms and lowering the level mod ℓ n

Luis Dieulefait, Xavier Taixés i Ventosa (2009)

Journal de Théorie des Nombres de Bordeaux

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In this article we study the behavior of inertia groups for modular Galois mod ℓ n representations and in some cases we give a generalization of Ribet’s lowering the level result (cf. []).