• Cyclotomic polynomials (in the parallel worlds of number theory) 

      Bamunoba, Alex Samuel (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 

      Randrianarisoa, Tovohery Hajatiana (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 ...
    • Elliptic curve cryptography 

      Louw, Gerard Jacques (Stellenbosch : Stellenbosch University, 2016-12)
      ENGLISH ABSTRACT : In this thesis we present a selection of Diffie-Hellman cryptosystems, which were classically formulated using the multiplicative group of a finite field, but which may be generalised to use other group ...
    • Geometric actions of the absolute Galois group 

      Joubert, Paul (Stellenbosch : University of Stellenbosch, 2006-03)
      This thesis gives an introduction to some of the ideas originating from A. Grothendieck's 1984 manuscript Esquisse d'un programme. Most of these ideas are related to a new geometric approach to studying the absolute ...
    • Geometry of Complex Polynomials: On Sendov's Conjecture 

      Chalebgwa, Taboka Prince (Stellenbosch : Stellenbosch University, 2016-12)
      ENGLISH ABSTRACT : Sendov’s conjecture states that if all the zeroes of a complex polynomial P(z) of degree at least two lie in the unit disk, then within a unit distance of each zero lies a critical point of P(z). In a ...
    • Riemann hypothesis for the zeta function of a function field over a finite field 

      Ranorovelonalohotsy, Marie Brilland Yann (Stellenbosch : Stellenbosch University, 2013-12)
      ENGLISH ABSTRACT: See the full text for the abstract