Arthur packets and the Ramanujan conjecture

Abstract

The purpose of this article is to show that under a part of the generalized Arthur’s $A$-packet conjecture, locally generic cuspidal automorphic representations of a quasi-split group over a number field are of Ramanujan type, that is, are tempered at almost all places. The $A$-packet conjecture allows one to reduce the problem to a special case of a general local question about the components of the corresponding Langlands $L$-packet which is then answered here in its generality.