EXPLICIT CONSTRUCTION OF RANKIN-COHEN-TYPE DIFFERENTIAL OPERATORS FOR VECTOR-VALUED SIEGEL MODULAR FORMS

On Rankin-cohen Brackets for Siegel Modular Forms

We determine an explicit formula for a Rankin-Cohen bracket for Siegel modular forms of degree n on a certain subgroup of the symplectic group. Moreover, we lift that bracket via a Poincaré series to a Siegel cusp form on the full symplectic group.

Rankin-Cohen Operators for Jacobi and Siegel Forms

For any non-negative integer v we construct explicitly ⌊v2⌋+1 independent covariant bilinear differential operators from Jk,m × Jk′,m′ to Jk+k′+v,m+m′ . As an application we construct a covariant bilinear differential operator mapping S (2) k ×S (2) k′ to S (2) k+k′+v. Here Jk,m denotes the space of Jacobi forms of weight k and index m and S (2) k the space of Siegel modular forms of degree 2 a...

Explicit Matrices for Hecke Operators on Siegel Modular Forms

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...

Some vector valued Siegel modular forms of genus 2

is a module over the ring of all modular forms with respect to the group Γ2[4, 8]. We are interested in its structure. By Igusa, the ring of modular forms is generated by the ten classical theta constants θ[m]. The module M contains a submodule N which is generated by 45 Cohen-Rankin brackets {θ[m], θ[n]}. We determine defining relations for this submodule and compute its Hilbert function (Theo...

Some vector valued Siegel modular forms of genus 3 Eberhard