Arthur Packets and Ramanujan Conjecture

We start by relating a result on the reducibility of induced representations of a reductive group through local Langlands correspondence to Artin L-functions. Such a result is of interest in the study of the arithmetic theory of intertwining operators and the Eisenstein cohomology in the work of Harder-Raghuram, and Raghuram and his collaborators. Moreover, assuming the Ramanujan conjecture for GL(n) over number fields, it shows that even locally generic cusp forms on a quasi-split group are tempered at almost all the places, making them parametrizing objects for cuspidal tempered packets. This is done by applying the above result to the theory of Arthur packets. These packets and their wavefront sets are now being studied in joint work with Baiying Liu, Alex Hazeltine, and Chi-Heng Lo, through Jiang's conjecture on these packets for classical groups. In the case of function fields, where Ramanujan is a theorem, one expects unconditional results as is evident from the recent work of Dan Ciubotaru and Michael Harris.



Purdue University