Representation Theory Seminar
This is Part II of the talk from September 20th. We will present the modified integrals to incorporate intertwining operator opposed to Fourier transform in the functional equation. In order to define analogous L-functions, we adopt the notion of "Good Sections" introduced by Piatetski- Shapiro and Rallis. We show that in Asai, exterior square and Rankin-Selberg cases, local factors via Rankin-Selberg integrals attached to either Schwartz-Bruhat functions or Good sections agree. We also propose a concept of exceptional poles in the context of good section which can be carried out on the analysis of symmetric square or cubic Asai L-functions.