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Mathematics  2010 

Arthur Packets and the Ramanujan Conjecture

DOI: 10.1215/0023608X-2010-018

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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.

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