The finite symplectic group Sp(2g) over the field of two elements has a natural representation on the vector space of Siegel modular forms of given weight for the principal congruence subgroup of level two. In this paper we decompose this representation, for various (small) values of the genus and the level, into irreducible representations. As a consequence we obtain uniqueness results for cer...

We present an explicit set of matrices giving the action of the Hecke operators T (p), Tj(p ) on Siegel modular forms. Introduction It is well-known that the space of elliptic modular forms of weight k has a basis of simultaneous eigenforms for the Hecke operators, and the Fourier coefficients of an eigenform (and hence the eigenform) are completely determined by its eigenvalues and first Fouri...

We introduce a differential operator invariant under the special linear group SL(2n, C), and, as a consequence, the symplectic group Sp(2n, C). Connections with generalized Rankin–Cohen brackets for Siegel modular forms of genus n are sketched.

© Université Bordeaux 1, 1995, tous droits réservés. L’accès aux archives de la revue « Journal de Théorie des Nombres de Bordeaux » (http://jtnb.cedram.org/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier do...

We introduce a differential operator invariant under the symplectic group Sp(2n, C). A connection with a Rankin Cohen bracket for Siegel modular forms of genus n is sketched.

We define a theta operator between spaces of Siegel modular forms (mod p), generalizing the theta operator for (elliptic) modular forms.

In this paper, we decompose the space of nearly holomorphic Hilbert-Siegel automorphic forms as representations adele group under certain assumptions. We also give an application for classical modular forms. particular, show surjectivity global Siegel operator congruence subgroups with large weights.

We study the hyperbolicity of compactifications of quotients of bounded symmetric domains by arithmetic groups. We prove that, up to an étale cover, they are Kobayashi hyperbolic modulo the boundary. Applying our techniques to Siegel modular varieties, we improve some former results of Nadel on the non-existence of certain level structures on abelian varieties over complex function fields.