Poles of Artin $L$-functions and the strong Artin conjecture

Abstract

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.

Authors

Andrew R. Booker

Department of Mathematics
Princeton University
Princeton, NJ 08544
United States