|
Abstract |
This is a notes for my lecture series at AMSS, July, 2014, on the Rankin-Selberg method and the theory of automorphic descents. In this series of eight lectures, I will discuss the Rankin-Selberg method for automorphic L-functions on one hand, and on the other hand, for the Langlands functoriality via the automorphic descents. The structure of Fourier coefficients of automorphic forms plays important role in the theory of automorphic descents, which includes the automorphic descents of Ginzburg -Rallis-Soudry and the joint work with Xu, Liu and Zhang on the special case of twisted automorphic descents. Finally, I will discuss how to bring the global Gan-Gross-Prasad conjecture into play in the general theory of twisted automorphic descents for general classical groups and discuss the relation of such a theory with the endoscopy classification theory of Arthur and Mok for the discrete spectrum of classical groups. |
