Koutsianas, Angelos (2016) Applications of S-unit equations to the arithmetic of elliptic curves. PhD thesis, University of Warwick.
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Abstract
Let K be a number field and S a finite set of prime ideals of K. By a classical result of Shafarevich ([Sil86]) we know that there are finitely many isomorphism classes ƸK;S of elliptic curves de ned over K with good reduction outside S. Many people have developed methods of computing ƸK;S explicitly. At the end, all the methods ask for solutions of specific Diophantine equations in order to determine ƸK;S. In this thesis we develop a new algorithmic method of computing EK;S by solving S{unit equations.
The method is implemented in the mathematical software Sage ([Dev16]) and examples are included in this thesis.
| Item Type: | Thesis [via Doctoral College] (PhD) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Library of Congress Subject Headings (LCSH): | Curves, Elliptic, Curves, Algebraic, K-theory, Diophantine equations, Algebraic number theory |
| Official Date: | September 2016 |
| Dates: | Date Event September 2016 Submitted |
| Institution: | University of Warwick |
| Theses Department: | Mathematics Institute |
| Thesis Type: | PhD |
| Publication Status: | Unpublished |
| Supervisor(s)/Advisor: | Cremona, J. E |
| Sponsors: | Akadēmia Athēnōn , Bekiari-Vekri Foundatio |
| Extent: | vii, 104 leaves. |
| Language: | eng |
| URI: | https://wrap.warwick.ac.uk/86760/ |
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