Cyclicity of elliptic curves over function fields

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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
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

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