Automorphic Lifts of Prescribed Types

AUTOMORPHY FOR SOME l-ADIC LIFTS OF AUTOMORPHIC

We extend the results of [CHT] by removing the ‘minimal ramification’ condition on the lifts. That is we establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge-Tate numbers), l-adic lifts of certain automorphic mod l Galois representations of any dimension. The main innovation is a new approach to the automorphy of non-minimal lifts which is closer in spi...

Automorphic representations with prescribed ramification for unitary groups

Let F be a totally real number field, n a prime integer, and G a unitary group of rank n defined over F that is compact at infinity. We prove an asymptotic formula for the number of automorphic representations of G whose factors at finitely many places are prescribed up to inertia. These factors are specified by local inertial types, and the proof relies crucially on a bound on the traces of th...

A Simple Case of Siegel-Weil Formula

• The theta correspondence 1 is a correspondence between automorphic forms on two members of a dual reductive pair. Because of the relation between automorphic forms and automor-phic representations, it is also a correspondence between automorphic representations. The Siegel-Weil formula says that certain natural linear combinations of theta lifts are Siegel-type holomorphic Eisenstein Series.

Automorphy for some l-adic lifts of automorphic modl Galois representations. II

Special Values of L-functions for Saito-kurokawa Lifts

In this paper we obtain special value results for L-functions associated to classical and paramodular Saito-Kurokawa lifts. In particular, we consider standard L-functions associated to Saito-Kurokawa lifts as well as degree eight L-functions obtained by twisting with an automorphic form defined on GL(2). The results are obtained by combining classical and representation theoretic arguments.