Abstract: The method of analytic continuation was initiated by Buzzard-Taylor to treat the icosahedral case of the Artin conjecture over Q. In this talk, I will explain how to extend this approach to the Hilbert case. Let p be an odd prime number, and F be a totally real field in which p is unramified. We prove that a p-adic Galois representation over F, which is residually ordinarily modular and saitsifies certain local conditions at p, comes from actually a Hilbert modular form of weight 1. For the moment, we only know how to treat the case where the Galois representation is tamely ramified at p. This is a joint work with Payman Kassaei and Shu Sasaki. I hope Payman will have explained the general principle, then I will focus on the details of the analytic continuation process.