Rankin-Cohen Type Differential Operators for Siegel Modular Forms

Details Rankin-Cohen Type Differential Operators for Siegel Modular Forms Rankin-Cohen Type Differential Operators for Siegel Modular Forms

1997-03-26

arxiv.org/abs/alg-geom/9703033v1

Mathematics

Algebraic Geometry

19 pages LaTeX2e using amssym.def

Scientific paper

Let H_n be the Siegel upper half space and let F and G be automorphic forms on H_n of weights k and l, respectively. We give explicit examples of differential operators D acting on functions on H_n x H_n such that the restriction of D(F(Z_1) G(Z_2)) to Z = Z_1 = Z_2 is again an automorphic form of weight k+l+v on H_n. 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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