Taylor, Richard

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