From Tate’s Thesis to Automorphic ForMS and Representations on GL(2)

Abstract

In this thesis we look at the celebrated Riemann-Zeta function and its generalizations and Tate’s famous thesis which gave a way to arrive at the functional equations and meromorphic continuouations of such functions. We do this by consider the local fields and finally come to the global result suing a suitable topology to glue things together. The next level of generalization is realizing functions on the upper half plane as Automorphic Representations of a general linear group where the representations are not only one-dimensional because of the non-commutativity of the space.