Now showing items 1-5 of 5
Cyclotomic polynomials (in the parallel worlds of number theory)
(Stellenbosch : Stellenbosch University, 2011-12)
ENGLISH ABSTRACT: It is well known that the ring of integers Z and the ring of polynomials A = Fr[T] over a finite field Fr have many properties in common. It is due to these properties that almost all the famous ...
Drinfeld modules and their application to factor polynomials
(Stellenbosch : Stellenbosch University, 2012-12)
ENGLISH ABSTRACT: Major works done in Function Field Arithmetic show a strong analogy between the ring of integers Z and the ring of polynomials over a nite eld Fq[T]. While an algorithm has been discovered to factor ...
On the coefficients of Drinfeld modular forms of higher rank
(Stellenbosch : Stellenbosch University, 2014-04)
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 ...
Explicit class field theory for rational function fields
(Stellenbosch : Stellenbosch University, 2008-12)
Class field theory describes the abelian extensions of a given field K in terms of various class groups of K, and can be viewed as one of the great successes of 20th century number theory. However, the main results in ...
An analogue of the Andre-Oort conjecture for products of Drinfeld modular surfaces
(Stellenbosch : Stellenbosch University, 2013-03)
ENGLISH ABSTRACT: This thesis deals with a function eld analog of the André-Oort conjecture. The (classical) André-Oort conjecture concerns the distribution of special points on Shimura varieties. In our case we consider ...