Modular Forms and L-functions

Abstract

In this thesis, our main aims are expressing some strong relations between modular forms, Hecke operators, and L-functions. We start with background information for modular forms and give some information about the linear space of modular forms. Next, we introduce Hecke operators and their properties. Also we find a basis of Hecke eigenforms. Then, we explain how to construct L-functions from modular forms. Finally, we give a nice functional equation for completed L-function.