Cyclotomic polynomials (in the parallel worlds of number theory)

dc.contributor.advisorBreuer, Florianen_ZA
dc.contributor.authorBamunoba, Alex Samuelen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.en_ZA
dc.descriptionThesis (MSc)--Stellenbosch University, 2011.en_ZA
dc.description.abstractENGLISH 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 (multiplicative) number theoretic results over Z have analogues over A. In this thesis, we are devoted to utilising this analogy together with the theory of Carlitz modules. We do this to survey and compare the analogues of cyclotomic polynomials, the size of their coefficients and cyclotomic extensions over the rational function field k = Fr(T).en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING: Dit is bekend dat Z, die ring van heelgetalle en A = Fr[T], die ring van polinome oor ’n eindige liggaam baie eienskappe in gemeen het. Dit is as gevolg van hierdie eienskappe dat feitlik al die bekende multiplikative resultate wat vir Z geld, analoë in A het. In hierdie tesis, fokus ons op die gebruik van hierdie analogie saam met die teorie van die Carlitz module. Ons doen dit om ’n oorsig oor die analoë van die siklotomiese polinome, hul koëffisiënte, en siklotomiese uitbreidings oor die rasionele funksie veld k = Fr(T).af_ZA
dc.format.extent71 p. : ill.
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.subjectCyclotomic polynomialsen_ZA
dc.subjectCarlitz modulesen_ZA
dc.subjectFunction fieldsen_ZA
dc.subjectDrinfeld modulesen_ZA
dc.subjectDissertations -- Mathematicsen_ZA
dc.subjectTheses -- Mathematicsen_ZA
dc.titleCyclotomic polynomials (in the parallel worlds of number theory)en_ZA
dc.rights.holderStellenbosch University

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