We construct certain C ∞-differential operators and their p-adic analogues, which
act on (vector- or scalar-valued) automorphic forms on the unitary groups U (n, n).
We study properties of these operators, and we prove some arithmeticity theorems
using them. These differential operators 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. They are a generalization to the vector-valued situation
of the p-adic differential operators constructed in the one-dimensional setting by N.
Katz. They should be useful in the construction of certain p-adic L-functions, in
particular p-adic L-functions attached to p-adic families of automorphic forms on
the unitary groups U (n)
× U (n).
Ph.D.
Mathematics
University of Michigan, Horace H. Rackham School of Graduate Studies
http://deepblue.lib.umich.edu/bitstream/2027.42/63860/1/eeischen_1.pdf