p-adic Differential Operators on Automorphic Forms on Unitary Groups

TL;DR

This paper develops p-adic differential operators for automorphic forms on U(n,n), extending previous work to higher dimensions and vector-valued forms, with potential applications in constructing p-adic L-functions.

Contribution

It introduces new p-adic differential operators on automorphic forms on U(n,n), generalizing earlier operators to higher-dimensional, vector-valued contexts.

Findings

Constructed p-adic differential operators for U(n,n) automorphic forms.

Extended Katz's operators from Hilbert modular forms to higher dimensions.

Potential applications in p-adic L-function construction.

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).