Karabina, Koray
(2005)
*Cyclicity of elliptic curves over function fields.*
[Thesis]

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## Abstract

Let K be a global function field over a finite field F containing q elements. Let E be an elliptic curve defined over K. For a prime P in K we can reduce the elliptic curve mod P and get an elliptic curve over a finite extension of F. The group of points on the reduced elliptic curve is either a cyclic group or it is a product of two cyclic groups. We determine the Dirichlet density of the primes in K such that the reduced curve has a cyclic group structure.

Item Type: | Thesis |
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Uncontrolled Keywords: | Function Fields. -- Zeta Functions. -- Elliptic Curves. -- Dirichlet Density |

Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences |

Depositing User: | IC-Cataloging |

Date Deposited: | 15 Apr 2008 15:38 |

Last Modified: | 26 Apr 2022 09:45 |

URI: | https://research.sabanciuniv.edu/id/eprint/8275 |