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Elliptic Surfaces with positive Mordell-Weil rank and Quadratic twists of elliptic curves / Mohamed Mohamed Alaa Eldin Mostafa ; Supervised Nabil L. Youssef , Mohammad M. Sadek

By: Contributor(s): Material type: TextTextLanguage: English Publication details: Cairo : Mohamed Mohamed Alaa Eldin Mostafa , 2017Description: 51 P. : charts ; 25cmOther title:
  • أسطح ناقصية ذات رتبة موجبة و الإنحرافات التربيعية للمنحنيات الناقصية [Added title page title]
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Dissertation note: Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics Summary: In 1922, Mordell proved that the group of rational points {u1D438}({u211A}), of an elliptic curve {u1D438}, is a finitely generated abelian group. While the finite part is well understood, the infinite part is much more mysterious. In this thesis we aim to deepen our understanding of the arithmetic of the group of rational points of elliptic curves by discussing certain arithmetic questions on elliptic curves. We investigate the existence of high length geometric progressions on elliptic and hyperelliptic curves. Moreover, we study ranks of quadratic twists of pairs of elliptic curves
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Thesis Thesis قاعة الرسائل الجامعية - الدور الاول المكتبة المركزبة الجديدة - جامعة القاهرة Cai01.12.17.M.Sc.2017.Mo.E (Browse shelf(Opens below)) Not for loan 01010110074847000
CD - Rom CD - Rom مخـــزن الرســائل الجـــامعية - البدروم المكتبة المركزبة الجديدة - جامعة القاهرة Cai01.12.17.M.Sc.2017.Mo.E (Browse shelf(Opens below)) 74847.CD Not for loan 01020110074847000

Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics

In 1922, Mordell proved that the group of rational points {u1D438}({u211A}), of an elliptic curve {u1D438}, is a finitely generated abelian group. While the finite part is well understood, the infinite part is much more mysterious. In this thesis we aim to deepen our understanding of the arithmetic of the group of rational points of elliptic curves by discussing certain arithmetic questions on elliptic curves. We investigate the existence of high length geometric progressions on elliptic and hyperelliptic curves. Moreover, we study ranks of quadratic twists of pairs of elliptic curves

Issued also as CD

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