TITLE: Recent developments on the Artin conjecture
QUESTION [14 upvotes]: Hi to everybody! I am studying right now the work of Serre and Deligne about the modularity of 2-dimensional complex Galois representations. I know that if $\rho \colon G_{\mathbb Q} \to GL_2(\mathbb C)$ is an irreducible Galois representation s.t. $\pi(\rho(G_{\mathbb Q}))$ is dihedral or isomorphic to $S_4$ or $A_4$ (where $\pi \colon GL_2(\mathbb C) \to PGL_2(\mathbb C)$ is the projection onto the quotient), then the Artin conjecture holds for $L(s,\rho)$, namely such function has an holomorphic continuation to the entire complex plane. So my question is: has the conjecture been proven (or disproven) in the case $\pi(\rho(G_{\mathbb Q})) \cong A_5$?
And moreover, I read that it is expected a more general result to be true, something called "strong Artin conjecture" which deals with cuspidal representations. Where can I find something introductory to this topic?

REPLY [5 votes]: Rogawski's article "Functoriality and the Artin Conjecture", available from his website, is a good introduction. It was published in 1997, but I think that Khare-Wintenberger is the only advance since then.
A bit more is known -- the Strong Artin Conjecture holds for $n$-dimensional representations of nilpotent Galois groups by Arthur-Clozel ("Simple algebras, base change, and the advanced theory of the trace formula").