Arthur Packets and the Ramanujan Conjecture

Abstract

The purpose of this paper is to show that under a part of generalized Arthur's A-packet conjecture, locally generic cuspidal automorphic representations of a quasisplit group over a number field are of Ramanujan type, i.e., 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.

References in corpus (1)

• Symmetry of Arthur parameters under Aubert involution

Cited by in corpus (8)

• A conjecture on Whittaker-Fourier coefficients of cusp forms
• Arithmeticity for periods of automorphic forms
• A strong multiplicity one theorem for SL(2)
• Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families
• Density of Self-Dual Automorphic Representations of GL_n(A_Q)
• R-group and Whittaker space of some genuine representations
• On the generic local Langlands correspondence for GSpin groups
• Structure of the Unramified L-packet