On fields of rationality for automorphic representations

On Strong Multiplicity One for Automorphic Representations

We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let π be a unitary, cuspidal, automorphic representation of GLn(AK). Let S be a set of finite places of K, such that the sum ∑ v∈S Nv −2/(n+1) is convergent. Then π is uniquely determined by the collection of the local components {πv | v 6∈ S, v finite} of π. Combining this theorem with base change, it is p...

Introduction to Automorphic Representations

Unipotent Automorphic Representations : Conjectures

In these notes, we shall attempt to make sense of the notions of semisimple and unipotent representations in the context of automorphic forms. Our goal is to formulate some conjectures, both local and global, which were originally motivated by the trace formula. Some of these conjectures were stated less generally in lectures [2] at the University of Maryland. The present paper is an update of ...

Automorphic Representations of Adele Groups

Automorphic Representations of Gsp(4)

1. In this note, we shall describe a classification for automorphic representations of GSp(4), the group of similitudes of four-dimensional symplectic space. The results are part of a project [A3] on the automorphic representations of general classical groups. The monograph [A3] is still in preparation. When complete, it will contain a larger classification of representations, subject to a gene...