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.
