The generalized doubling method: local theory

A fundamental difficulty in the study of automorphic representations, representations of p-adic groups and the Langlands program is to handle the non-generic case. In a recent collaboration with David Ginzburg, we presented a new integral representation for the tensor product L-functions of G×GLk where G is a classical group, that applies to all cuspidal automorphic representations, generic or otherwise. In this work we develop the local theory of these integrals, define the local γ-factors and provide a complete description of their properties. We can then define L- and ϵ-factors at all places, and as a consequence obtain the global completed L-function and its functional equation.