On tensor product L-functions and Langlands functoriality

Abstract. In the spirit of the Langlands proposal on Beyond Endoscopy, we discuss the explicit relation between the Langlands functorial transfers and automorphic L-functions. It is well-known that the poles of the Lfunctions have deep impact to the Langlands functoriality. Our discussion also includes the meaning of the central value of the tensor product Lfunctions in terms of the Langlands functoriality. This leads to the theory of the twisted automorphic descents for cuspidal automorphic representations of general classical groups