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Applications of S-unit equations to the arithmetic of elliptic curves
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Koutsianas, Angelos (2016) Applications of S-unit equations to the arithmetic of elliptic curves. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3057766~S1
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 (PhD) | ||||
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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: |
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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Publication Status: | Unpublished | ||||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 |
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