W. Eholzer et T. Ibukiyama, RANKIN-COHEN TYPE DIFFERENTIAL-OPERATORS FOR SIEGEL MODULAR-FORMS, International journal of mathematics, 9(4), 1998, pp. 443-463
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.