Date of Award
5-2010
Document type
dissertation
Access Type
Open Access Dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
First Advisor
Tom Weston
Second Advisor
Farshid Hajir
Third Advisor
Siman Wong
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.
DOI
https://doi.org/10.7275/1557646
Recommended Citation
Ridgdill, Penny Catherine, "On the Frequency of Finitely Anomalous Elliptic Curves" (2010). Open Access Dissertations. 238.
https://doi.org/10.7275/1557646
https://scholarworks.umass.edu/open_access_dissertations/238