Rankin-Cohen Type Differential Operators for Siegel Modular Forms
Abstract
Let Hn be the Siegel upper half space and let F and G be automorphic forms on Hn of weights k and l, respectively. We give explicit examples of differential operators D acting on functions on Hn x Hn such that the restriction of D(F(Z1) G(Z2)) to Z = Z1 = Z2 is again an automorphic form of weight k+l+v on Hn. Since the elliptic case, i.e. n=1, has already been studied some time ago by R. Rankin and H. Cohen we call such differential operators Rankin-Cohen type operators. We also discuss a generalisation of Rankin-Cohen type operators to vector valued differential operators.
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