Date of Award
Doctor of Philosophy (PhD)
Anomalous Primes, Elliptic Curve Cryptography, Elliptic Curves, Galois Representations, Number Theory
Mathematics | Statistics and Probability
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.
Ridgdill, Penny Catherine, "On the Frequency of Finitely Anomalous Elliptic Curves" (2010). Open Access Dissertations. Paper 238.