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Description
Title: | Algorithmic Aspects of Biquadratic, Cubic and Radical Function Fields |
Author(s): | Wu, Qingquan |
Doctoral Committee Chair(s): | Ullom, Stephen V. |
Department / Program: | Mathematics |
Discipline: | Mathematics |
Degree Granting Institution: | University of Illinois at Urbana-Champaign |
Degree: | Ph.D. |
Genre: | Dissertation |
Subject(s): | Mathematics |
Abstract: | 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. |
Issue Date: | 2007 |
Type: | Text |
Language: | English |
Description: | 112 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. |
URI: | http://hdl.handle.net/2142/86897 |
Other Identifier(s): | (MiAaPQ)AAI3301251 |
Date Available in IDEALS: | 2015-09-28 |
Date Deposited: | 2007 |
This item appears in the following Collection(s)
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Dissertations and Theses - Mathematics
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Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois