On tensor product $L$-functions and Langlands functoriality

Document Type: Special Issue of BIMS in Honor of Professor Freydoon Shahidi

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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.
 

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