Thesis (PhD)--Stellenbosch University, 2014. / 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. / AFRIKAANSE OPSOMMING: Drinfeld modulêre vorme van rang 2 word al vir meer as 30 jaar bestudeer
en alhoewel dit lankal bekend is dat daar Drinfeld modulêre vorme van hoër
rang moet bestaan, is die de nisie eers onlangs vasgepen. In 1988 het Gekeler
die artikel [Ge2] gepubliseer waarin hy die koeffisiënte van Fourier reekse van
rang 2 Drinfeld modulêre vorme bestudeer. Die doel van hierdie proefskrif is
om dieselfde studie vir Drinfeld modulêre vorme van hoër rang uit te voer.
Die hoofresultate is dat die koeffi siënte self (swak) Drinfeld modulêre
vorme is, `n produk formule vir die diskriminant funksie, die feit dat sekere
natuurlik gede finiëerde modulêre vorme rasionaal is, en die vasstelling van
Hecke eievorme en hul eiewaardes.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/86387 |
| Date | 04 1900 |
| Creators | Basson, Dirk Johannes |
| Contributors | Breuer, Florian, Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | 89 p. |
| Rights | Stellenbosch University |
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