Algorithmic Aspects of Biquadratic, Cubic and Radical Function Fields

"Above all, our work presents very explicit results, mostly stated as formulae and explicit representations, rather than algorithms. The formulae that we obtained for the ramifications and an integral basis of a cyclic biquadratic function field are simple, explicit and efficient. The computation of the unit group on a global bicyclic biquadratic function field generalizes and simplifies Kubota's work [Kub56) to function fields. It thus settles this question for all global bicyclic biquadratic extensions. The explicit construction of an integral basis of a radical function field is efficient and has a ""diagonal with denominators"" form, which is the simplest form that one can expect. This type of basis has no number field analogue."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Wu, Qingquan

Contributors dc:contributor

• Ullom, Stephen V.

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3301251

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86897