On the Ramanujan conjecture over number fields

Details On the Ramanujan conjecture over number fields On the Ramanujan conjecture over number fields

2010-03-02

arxiv.org/abs/1003.0559v4

Mathematics

Number Theory

Minor corrections from previous version. To appear in Annals of Mathematics

Scientific paper

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.

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