• An analogue of the Andre-Oort conjecture for products of Drinfeld modular surfaces 

      Karumbidza, Archie (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 ...
    • Drinfeld modular forms of higher rank from a lattice-oriented point of view 

      Baker, Liam Bradwin (Stellenbosch : Stellenbosch University., 2020-04)
      ENGLISH ABSTRACT: Please refer to full text for abstract
    • Explicit class field theory for rational function fields 

      Rakotoniaina, Tahina (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 ...
    • On the coefficients of Drinfeld modular forms of higher rank 

      Basson, Dirk Johannes (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 ...
    • On the Latimer-MacDuffee theorem for polynomials over finite fields 

      Van Zyl, Jacobus Visser (Stellenbosch : University of Stellenbosch, 2011-03)
      ENGLISH ABSTRACT: Latimer & MacDuffee showed in 1933 that there is a one-to-one correspondence between equivalence classes of matrices with a given minimum polynomial and equivalence classes of ideals of a certain ring. ...
    • Torsion bounds for Drinfeld modules with complex multiplication 

      Rabenantoandro, Andry Nirina (Stellenbosch : Stellenbosch University., 2020-04)
      ENGLISH ABSTRACT: The main objective of the present thesis is to prove an analogue for Drinfeld modules of a theorem due to Clark and Pollack. The cardinality of the group of K-rational torsion points of an elliptic curve ...