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p -adic Differential Operators on Automorphic Forms on Unitary Groups

Ellen E. Eischen (2012)

Annales de l’institut Fourier

The goal of this paper is to study certain p -adic differential operators on automorphic forms on U ( n , n ) . These operators are a generalization to the higher-dimensional, vector-valued situation of the p -adic differential operators constructed for Hilbert modular forms by N. Katz. They are a generalization to the p -adic case of the C -differential operators first studied by H. Maass and later studied extensively by M. Harris and G. Shimura. The operators should be useful in the construction of certain p -adic...

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