Browsing by Author "Bamunoba, Alex Samuel"

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    Arithmetic of carlitz polynomials
    (Stellenbosch : Stellenbosch University, 2014-12) Bamunoba, Alex Samuel; Keet, Arnold; Stellenbosch University. Faculty of Economic and Management Sciences. Department of Africa Centre for HIV/AIDS Management.
    ENGLISH ABSTRACT: See pdf for abstract
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    Cyclotomic polynomials (in the parallel worlds of number theory)
    (Stellenbosch : Stellenbosch University, 2011-12) Bamunoba, Alex Samuel; Breuer, Florian; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
    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 (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).