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On the coefficients of Drinfeld modular forms of higher rank
Thesis (PhD)--Stellenbosch University, 2014.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2014
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| _version_ | 1867613737756655616 |
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| access_status_str | Open Access |
| author | Basson, Dirk Johannes |
| author2 | Breuer, Florian |
| author_browse | Basson, Dirk Johannes Breuer, Florian |
| author_facet | Breuer, Florian Basson, Dirk Johannes |
| author_sort | Basson, Dirk Johannes |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (PhD)--Stellenbosch University, 2014. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/86387 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:40:54.381Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/86387 On the coefficients of Drinfeld modular forms of higher rank Basson, Dirk Johannes Breuer, Florian Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Drinfeld modular forms modular forms Drinfeld modules Moduli spaces Dissertations -- Mathematics Theses -- Mathematics Drinfeld modules 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. Doctoral 2014-04-16T17:29:09Z 2014-04-16T17:29:09Z 2014-04 Thesis http://hdl.handle.net/10019.1/86387 en_ZA Stellenbosch University 89 p. application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Drinfeld modular forms modular forms Drinfeld modules Moduli spaces Dissertations -- Mathematics Theses -- Mathematics Drinfeld modules Basson, Dirk Johannes On the coefficients of Drinfeld modular forms of higher rank |
| title | On the coefficients of Drinfeld modular forms of higher rank |
| title_full | On the coefficients of Drinfeld modular forms of higher rank |
| title_fullStr | On the coefficients of Drinfeld modular forms of higher rank |
| title_full_unstemmed | On the coefficients of Drinfeld modular forms of higher rank |
| title_short | On the coefficients of Drinfeld modular forms of higher rank |
| title_sort | on the coefficients of drinfeld modular forms of higher rank |
| topic | Drinfeld modular forms modular forms Drinfeld modules Moduli spaces Dissertations -- Mathematics Theses -- Mathematics Drinfeld modules |
| url | http://hdl.handle.net/10019.1/86387 |
| work_keys_str_mv | AT bassondirkjohannes onthecoefficientsofdrinfeldmodularformsofhigherrank |