p-adic Differential Operators on Automorphic Forms on Unitary Groups

Abstract

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).

Cited by in corpus (10)

• p-adic L-functions for unitary groups
• p-adic Eisenstein series and L-functions of certain cusp forms on definite unitary groups
• Theta operators on unitary Shimura varieties
• Differential operators, pullbacks, and families of automorphic forms
• p-adic q-expansion principles on unitary Shimura varieties
• A p-adic Eisenstein measure for vector-weight automorphic forms
• Differential operators mod $p$: analytic continuation and consequences
• Entire theta operators at unramified primes
• Derivative of the standard $p$-adic $L$-function associated with a Siegel form
• An introduction to Eisenstein measures