### Analytic Characterization of Riemann Zeta Function

By Wei Pin Wong

April 26, 2012

#### Abstract

Riemann's Theorem says that the Riemann Zeta function has three important analytic properties, namely the analytic continuation, functional equation and boundedness. In this seminar, I'll talk about Hamburger's Theorem, which says that any Dirichlet's series that satisfies these properties is just the Riemann Zeta function up to scalar multiplication. If time permits, I'll talk about generalization of this converse theorem to L-functions and Dedekind Zeta functions.