RANKIN-COHEN TYPE DIFFERENTIAL-OPERATORS FOR SIEGEL MODULAR-FORMS

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 exampl es of differential operators D acting on functions on H-n x H-n such t hat the restriction of D(F(Z(1))G(Z(2))) to Z = Z(1) = Z(2) is again a n 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 operato rs. We also discuss a generalisation of Rankin-Cohen type operators to vector valued differential operators.