The Langlands-Shahidi method over function fields and applications

We present the Langlans-Shahidi method for the study of automorphic L-functions over aglobal function field. We will look at an interesting case, where we study exterior and symmetric square L-functions. We show that our L-functions and root numbers are compatible with the local Langlands correspondence for GL(n). In addition, there is a transfer or switch of characteristic between close local fields of characteristic zero and characteristic p. Furthermore, there are interesting applications to the classical groups. This includes a proof of the Ramanujan conjecture over function fields.