Geodesic
Poles of Artin $L$-functions and the strong Artin conjecture
Andrew R. Booker1
1 Department of Mathematics, Princeton University, Princeton, NJ 08544, United States
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.
DOI : 10.4007/annals.2003.158.1089

Andrew R. Booker 1

1 Department of Mathematics, Princeton University, Princeton, NJ 08544, United States 
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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. http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.158.1089/

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