الفهرس Only 14 pages are availabe for public view
 |  | from | 62 |  |  |
| | | from | 62 | | |
Abstract
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