p-adic Differential Operators on Automorphic Forms on Unitary Groups

Details p-adic Differential Operators on Automorphic Forms on Unitary Groups p-adic Differential Operators on Automorphic Forms on Unitary Groups

2010-06-25

arxiv.org/abs/1006.4898v1

Mathematics

Number Theory

79 pages

Scientific paper

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^{\infty}-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 L-functions attached to p-adic families of automorphic forms on the unitary groups U(n) x U(n).

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