Rankin-Cohen type differential operators for Siegel modular forms
Rankin-Cohen type differential operators for Siegel modular forms
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DOI：
10.1142/s0129167x98000191
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发表时间：
1997-03
影响因子：
0.6
通讯作者：
Wolfgang Eholzer;T. Ibukiyama
中科院分区：
文献类型：
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作者：
Wolfgang Eholzer;T. Ibukiyama
设n是Siegel上半空间，F和G分别是n上权为k和l的自守形式。我们给出了微分算子D作用在n × n上的函数的显式例子，使得对Z = Z1 = Z2的限制又是n上权k + l + v的自守形式。由于椭圆情形，即n = 1，已经研究了一段时间前由R。兰金和H.我们称这种微分算子为Rankin-Cohen型算子。我们还讨论了Rankin-Cohen型算子到向量值微分算子的推广。
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 × ℍn such that the restriction of 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.