p-adic Differential Operators on Automorphic Forms on Unitary Groups
Number Theory
2013-02-01 v2
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).
Cite
@article{arxiv.1006.4898,
title = {p-adic Differential Operators on Automorphic Forms on Unitary Groups},
author = {Ellen E. Eischen},
journal= {arXiv preprint arXiv:1006.4898},
year = {2013}
}