On the meromorphic continuation of degree two $L$-functions
Doc. Math. (Bielefeld) Extra Vol. John H. Coates' Sixtieth Birthday, 729-779 (2006)
We prove that the L-function of any regular (distinct Hodge numbers), irreducible, rank two motive over the rational numbers has meromorphic continuation to the whole complex plane and satisfies the expected functional equation.
Mathematics Subject Classification
11R39, 11F80, 11G40, 11F41, 11F70
Galois representation, modularity, $L$-function, meromorphic continuation, Fontaine-Mazur conjecture, Hilbert modular form