Rankin-Cohen Type Differential Operators for Siegel Modular Forms
alg-geom
2008-02-03 v1 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.alg-geom/9703033,
title = {Rankin-Cohen Type Differential Operators for Siegel Modular Forms},
author = {W. Eholzer and T. Ibukiyama},
journal= {arXiv preprint arXiv:alg-geom/9703033},
year = {2008}
}
Comments
19 pages LaTeX2e using amssym.def