Doubling constructions: Global functoriality for non-generic cuspidal representations

We study the generalized doubling method for pairs of representations of G × GLk where G is a symplectic group, split special orthogonal groupor split general spin group. We analyze the poles of the local integrals andprove that the global completed L-function with a cuspidal representationof GLk twisted by a highly ramified Hecke character is entire. We obtaina new proof of the weak functorial transfer of cuspidal automorphic representations of G to the natural general linear group, which is independent of the trace formula and its prerequisites, by combining our results with the Converse Theorem.