Poles of Artin $L$-functions and the strong Artin conjecture
Annals of mathematics, Tome 158 (2003) no. 3, pp. 1089-1098
Voir la notice de l'article provenant de la source Annals of Mathematics website
We show that if the $L$-function of an irreducible 2-dimensional complex Galois representation over $\mathbb{Q}$ is not automorphic then it has infinitely many poles. In particular, the Artin conjecture for a single representation implies the corresponding strong Artin conjecture.
@article{10_4007_annals_2003_158_1089,
author = {Andrew R. Booker},
title = {Poles of {Artin} $L$-functions and the strong {Artin} conjecture},
journal = {Annals of mathematics},
pages = {1089--1098},
publisher = {mathdoc},
volume = {158},
number = {3},
year = {2003},
doi = {10.4007/annals.2003.158.1089},
mrnumber = {2031863},
zbl = {1081.11038},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.158.1089/}
}
TY - JOUR AU - Andrew R. Booker TI - Poles of Artin $L$-functions and the strong Artin conjecture JO - Annals of mathematics PY - 2003 SP - 1089 EP - 1098 VL - 158 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.158.1089/ DO - 10.4007/annals.2003.158.1089 LA - en ID - 10_4007_annals_2003_158_1089 ER -
%0 Journal Article %A Andrew R. Booker %T Poles of Artin $L$-functions and the strong Artin conjecture %J Annals of mathematics %D 2003 %P 1089-1098 %V 158 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.158.1089/ %R 10.4007/annals.2003.158.1089 %G en %F 10_4007_annals_2003_158_1089
Andrew R. Booker. Poles of Artin $L$-functions and the strong Artin conjecture. Annals of mathematics, Tome 158 (2003) no. 3, pp. 1089-1098. doi: 10.4007/annals.2003.158.1089
Cité par Sources :