Separators of Siegel modular forms of degree two

We prove that cuspidal Siegel modular forms of degree two and weight are uniquely determined by their Fourier coefficients on small subsets of matrices of content one. This generalizes results of Breulmann, Kohnen, Katsurada, Scharlau and Walling. We give applications to the space of Saito-Kurokawa lifts.

     

Arithmetic behaviour of Hecke eigenvalues of Siegel cusp forms of degree two

The Ramanujan Journal - Let F and G be Siegel cusp forms for $${mathrm{Sp}}_4({{mathbb {Z}}})$$ and weights $$k_1, k_2$$ , respectively. Also let F and G be Hecke eigenforms lying in distinct...     

On Fourier coefficients of Siegel modular forms of degree two with respect to congruence subgroups

We prove a formula of Petersson’s type for Fourier coefficients of Siegel cusp forms of degree 2 with respect to congruence subgroups, and as a corollary, show upper bound estimates of individual Fourier coefficients. The method in this paper is essentially a generalization of Kitaoka’s previous work which studied the full modular case, but some modification is necessary to obtain estimates which are sharp with respect to the level aspect.     

Siegel modular forms of degree 2 over rings

Based on moduli theory of abelian varieties, extending Igusa's result on Siegel modular forms over C, we describe the ring of Siegel full modular forms of degree 2 over any Z-algebra in which 6 is invertible.     

Siegel cusp forms of degree 12k and weight 12k

In this paper we prove the existence of cusp forms relative to the full modular group whose genus is equal to the weight. These cusp forms are linear combination of theta series. Received: 26 July 1999 / Revised version: 16 September 1999     

On characteristic twists of multiple Dirichlet series associated to Siegel cusp forms

We define a twisted two complex variables Rankin-Selberg convolution of Siegel cusp forms of degree 2. We find its group of functional equations and prove its analytic continuation to . As an application we obtain a non-vanishing result for special values of the Fourier Jacobi coefficients. We also prove the analytic properties for the characteristic twists of convolutions of Jacobi cusp forms. Research Supported by Fondecyt grants 1061147, 7060241.