Hi to everybody! I am studying right now the work of Serre and Deligne about the modularity of 2dimensional 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?
The remaining $A_5$ case of the strong Artin conjecture was recently settled by Khare and Wintenberger, see Corollary 10.2 in their paper Serre's modularity conjecture (I), Invent. Math. 178 (2009), 485504. I should add that the proof is very complicated and builds on the deep work of many others (I started to make a list here, but then stopped as it would be quite long and probably incomplete). 


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 KhareWintenberger 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 ArthurClozel ("Simple algebras, base change, and the advanced theory of the trace formula"). 

