Displaying similar documents to “Surjectivity of Siegel Φ -operator for square free level and small weight”

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.

Quasimodular forms: an introduction

Emmanuel Royer (2012)

Annales mathématiques Blaise Pascal

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Quasimodular forms were the heroes of a Summer school held June 20 to 26, 2010 at Besse et Saint-Anastaise, France. We give a short introduction to quasimodular forms. More details on this topics may be found in [].

Geometric and p -adic Modular Forms of Half-Integral Weight

Nick Ramsey (2006)

Annales de l’institut Fourier

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In this paper we introduce a geometric formalism for studying modular forms of half-integral weight. We then use this formalism to define p -adic modular forms of half-integral weight and to construct p -adic Hecke operators.

Congruences for Siegel modular forms

Dohoon Choi, YoungJu Choie, Olav K. Richter (2011)

Annales de l’institut Fourier

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We employ recent results on Jacobi forms to investigate congruences and filtrations of Siegel modular forms of degree 2 . In particular, we determine when an analog of Atkin’s U ( p ) -operator applied to a Siegel modular form of degree 2 is nonzero modulo a prime p . Furthermore, we discuss explicit examples to illustrate our results.

A generalization of level-raising congruences for algebraic modular forms

Claus Mazanti Sorensen (2006)

Annales de l’institut Fourier

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In this paper, we extend the results of Ribet and Taylor on level-raising for algebraic modular forms on the multiplicative group of a definite quaternion algebra over a totally real field F . We do this for automorphic representations of an arbitrary reductive group G over F , which is compact at infinity. In the special case where G is an inner form of GSp ( 4 ) over ℚ , we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.