Drinfeld modular function

Abstract

In 1973, Drinfeld introduced the notion of elliptic modules, which are now known as Drinfeld modules. After that the analogies between number fields and function fields have many interesting new aspects. In the first part of this thesis, we establish some properties of Drinfeld modular functions in analogy with those obtained by Shimura and Berndt respectively. In the second part of this thesis, we will show that the coefficients of the Drinfeld modular equation $φ_n$ is not bounded as the degree of n goes to infinity. We also give an upper bound of the coefficients of the Drinfeld modular equation $φ_n$.