On icosahedral Artin representations

Abstract

If ρ : Gal(ℚac/ℚ))→GL2(ℂ) is a continuous odd irreducible representation wit nonsolvable image, then under certain local hypotheses we prove that ρ is the representation associated to a weight 1 modular form and hence that the L-function of ρ has an analytic continuation to the entire complex plane.