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 $L$-functions have deep impact to the Langlands functoriality‎. ‎Our discussion also‎ ‎includes the meaning of the central value of the tensor product $L$-functions in terms of the Langlands functoriality‎. ‎This‎ ‎leads to the theory of the twisted automorphic descents for cuspidal automorphic representations of general classical groups‎.<br />