The Selberg Class - An Introduction

I will discuss the structure of the Selberg class - in which certain expected properties of Dirichlet series and L-functions are axiomatised - along with the numerous interesting conjectures concerning the Dirichlet series in the Selberg class. Furthermore, results regarding the degree of the elements in the Selberg class shall be explored, culminating in the recent work of Kaczorowski and Perelli in which they prove the absence of elements with degree between one and two.