On the coefficients of Drinfeld modular forms of higher rank

Basson, Dirk Johannes (2014-04)

Thesis (PhD)--Stellenbosch University, 2014.

Thesis

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.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/86387
This item appears in the following collections: