L-functions and Functoriality

In my previous talk, I described the partial L-functions of cuspidal automorphic representations and said that their conjectured meromorphic continuation is important for the theory of automorphic forms. I then talked about integral representations as a method for proving this meromorphic continuation.

In this talk (which will be mostly independent of the previous one), I will describe a softened version of functoriality (which is the main theme in the Langlands program) and how L-functions help to detect and construct instances of functoriality.