Applications of S-unit equations to the arithmetic of elliptic curves

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 explicitl...

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Main Author:	Koutsianas, Angelos
Published:	University of Warwick 2016
Subjects:	516.3 QA Mathematics
Online Access:	http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707403

id	ndltd-bl.uk-oai-ethos.bl.uk-707403
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spelling	ndltd-bl.uk-oai-ethos.bl.uk-7074032018-07-24T03:15:31ZApplications of S-unit equations to the arithmetic of elliptic curvesKoutsianas, Angelos2016Let 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.516.3QA MathematicsUniversity of Warwickhttp://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707403http://wrap.warwick.ac.uk/86760/Electronic Thesis or Dissertation
collection	NDLTD
sources	NDLTD
topic	516.3 QA Mathematics
spellingShingle	516.3 QA Mathematics Koutsianas, Angelos Applications of S-unit equations to the arithmetic of elliptic curves
description	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.
author	Koutsianas, Angelos
author_facet	Koutsianas, Angelos
author_sort	Koutsianas, Angelos
title	Applications of S-unit equations to the arithmetic of elliptic curves
title_short	Applications of S-unit equations to the arithmetic of elliptic curves
title_full	Applications of S-unit equations to the arithmetic of elliptic curves
title_fullStr	Applications of S-unit equations to the arithmetic of elliptic curves
title_full_unstemmed	Applications of S-unit equations to the arithmetic of elliptic curves
title_sort	applications of s-unit equations to the arithmetic of elliptic curves
publisher	University of Warwick
publishDate	2016
url	http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707403
work_keys_str_mv	AT koutsianasangelos applicationsofsunitequationstothearithmeticofellipticcurves
_version_	1718714601435037696

Applications of S-unit equations to the arithmetic of elliptic curves

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