Cyclotomic polynomials (in the parallel worlds of number theory)

[摘要] ENGLISH ABSTRACT: It is well known that the ring of integers Z and the ring of polynomials A = Fr[T] over afinite field Fr have many properties in common. It is due to these properties that almost allthe famous (multiplicative) number theoretic results over Z have analogues over A. In thisthesis, 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 theircoefficients and cyclotomic extensions over the rational function field k = Fr(T).

[发布机构] Stellenbosch University