On the Meromorphic Continuation of Degree Two L-Functions

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.

2000 Mathematics Subject Classification: 11R39, 11F80, 11G40.

Keywords and Phrases: Galois representation, modularity, L-function, meromorphic continuation.

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