The Theory of Modular Forms and the Converse Theorem of Weil

Abstract

In this thesis we provide an introduction to the theory of modular forms. We aim to show two major results. The first one shows that the space of modular forms is finite dimensional. The second result is the “Converse Theorem of Weil” on L-functions associated to modular forms. As we go on we will encounter some very interesting mathematical objects such as modular curves, Hecke operators and L-functions.