Date of Award
Doctor of Philosophy (PhD)
James, Kevin L
Calkin , Neil
Maharaj , Hiren
Matthews , Gretchen
This dissertation presents results related to two problems in the arithmetic of elliptic curves.
Feng and Xiong equate the nontriviality of the Selmer groups associated with congruent number curves to the presence of certain types of partitions of graphs associated with the prime factorization of n. The triviality of the Selmer groups associated to the congruent number curve implies that the curve has rank zero which in turn implies n is noncongruent. We extend the ideas of Feng and Xiong in order to compute the Selmer groups of congruent number curves.
We prove an average version of a generalization of the Lang-Trotter conjecture for elliptic curves over number fields. For the of degree one and degree two primes we calculate an explicit constant.
Faulkner, Bryan, "ESTIMATES RELATED TO THE ARITHMETIC OF ELLIPTIC CURVES" (2007). All Dissertations. 105.