Geodesic
On the Ramanujan conjecture over number fields
Valentin Blomer1 ; Farrell Brumley2
1 Mathematisches Institut<br/> Universität Göttingen<br/> 37073 Göttingen<br/> Germany
2 Institut Élie Cartan<br/> Université Henri Poincaré Nancy 1<br/> 54506 Vandœuvre-les-Nancy<br/> France
Annals of mathematics, Tome 174 (2011) no. 1, pp. 581-605.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We extend to an arbitrary number field the best known bounds towards Ramanujan for the group $\mathrm{GL}_n$, $n=2,3,4$. In particular, we present a technique which overcomes the analytic obstacles posed by the presence of an infinite group of units.
DOI : 10.4007/annals.2011.174.1.18

Valentin Blomer 1 ; Farrell Brumley 2

1 Mathematisches Institut<br/> Universität Göttingen<br/> 37073 Göttingen<br/> Germany
2 Institut Élie Cartan<br/> Université Henri Poincaré Nancy 1<br/> 54506 Vandœuvre-les-Nancy<br/> France 
@article{10_4007_annals_2011_174_1_18,
     author = {Valentin Blomer and Farrell Brumley},
     title = {On the {Ramanujan} conjecture over number fields},
     journal = {Annals of mathematics},
     pages = {581--605},
     publisher = {mathdoc},
     volume = {174},
     number = {1},
     year = {2011},
     doi = {10.4007/annals.2011.174.1.18},
     mrnumber = {2811610},
     zbl = {05960712},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.174.1.18/}
}
TY  - JOUR
AU  - Valentin Blomer
AU  - Farrell Brumley
TI  - On the Ramanujan conjecture over number fields
JO  - Annals of mathematics
PY  - 2011
SP  - 581
EP  - 605
VL  - 174
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.174.1.18/
DO  - 10.4007/annals.2011.174.1.18
LA  - en
ID  - 10_4007_annals_2011_174_1_18
ER  - 
%0 Journal Article
%A Valentin Blomer
%A Farrell Brumley
%T On the Ramanujan conjecture over number fields
%J Annals of mathematics
%D 2011
%P 581-605
%V 174
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.174.1.18/
%R 10.4007/annals.2011.174.1.18
%G en
%F 10_4007_annals_2011_174_1_18
Valentin Blomer; Farrell Brumley. On the Ramanujan conjecture over number fields. Annals of mathematics, Tome 174 (2011) no. 1, pp. 581-605. doi : 10.4007/annals.2011.174.1.18. http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.174.1.18/

Cité par Sources :