(Stellenbosch : Stellenbosch University, 2014-04) Basson, Dirk Johannes; Breuer, Florian; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
ENGLISH ABSTRACT: Rank 2 Drinfeld modular forms have been studied for more than 30 years, and
while it is known that a higher rank theory could be possible, higher rank
Drinfeld modular forms have only recently been de ned. In 1988 Gekeler
published [Ge2] in which he studies the coe cients of rank 2 Drinfeld modular
forms. The goal of this thesis is to perform a similar study of the coe cients
of higher rank Drinfeld modular forms.
The main results are that the coe cients themselves are (weak) Drinfeld
modular forms, a product formula for the discriminant function, the rationality
of certain naturally de ned modular forms, and the computation of
some Hecke eigenforms and their eigenvalues.