Date of Award

5-2010

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Mathematics

First Advisor

Tom Weston

Second Advisor

Farshid Hajir

Third Advisor

Siman Wong

Keywords

Anomalous Primes, Elliptic Curve Cryptography, Elliptic Curves, Galois Representations, Number Theory

Subject Categories

Mathematics | Statistics and Probability

Abstract

Given an elliptic curve E over Q, we can then consider E over the finite field Fp. If Np is the number of points on the curve over Fp, then we define ap(E) = p+1-Np. We say primes p for which ap(E) = 1 are anomalous. In this paper, we search for curves E so that this happens for only a finite number of primes. We call such curves finitely anomalous. This thesis deals with the frequency of their occurrence and finds several examples.