On the Ramanujan conjecture over number fields
Number Theory
2011-03-16 v4 Representation Theory
Abstract
We extend to an arbitrary number field the best known bounds towards the Ramanujan conjecture for the groups GL(n), n=2, 3, 4. In particular, we present a technique which overcomes the analytic obstacles posed by the presence of an infinite group of units.
Cite
@article{arxiv.1003.0559,
title = {On the Ramanujan conjecture over number fields},
author = {Valentin Blomer and Farrell Brumley},
journal= {arXiv preprint arXiv:1003.0559},
year = {2011}
}
Comments
Minor corrections from previous version. To appear in Annals of Mathematics