Vector valued Siegel modular forms and their <i>L</i>-functions; Application of a differential operator

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

A Note on the Growth of Nearly Holomorphic Vector-valued Siegel Modular Forms

Let F be a nearly holomorphic vector-valued Siegel modular form of weight ρ with respect to some congruence subgroup of Sp2n(Q). In this note, we prove that the function on Sp2n(R) obtained by lifting F has the moderate growth (or “slowly increasing”) property. This is a consequence of the following bound that we prove: ‖ρ(Y )F (Z)‖ ∏n i=1(μi(Y ) λ1/2 + μi(Y ) −λ1/2) where λ1 ≥ . . . ≥ λn is th...

Vector-valued modular forms associated to linear ordinary differential equations

We consider a class of linear ordinary differential equations determined by a modular form of weight one, and construct vector-valued modular forms of weight two by using solutions of such differential equations.

A Theta Operator for Siegel Modular Forms (preliminary Version)

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