English

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.

Keywords

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

R2 v1 2026-06-21T14:52:50.466Z