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On a conjecture for the distributions of primes associated with elliptic curves

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On a conjecture for the distributions of primes associated with elliptic curves

Porter, Jeremy Graham (2009) On a conjecture for the distributions of primes associated with elliptic curves. Masters thesis, Concordia University.

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Abstract

For an elliptic curve E and fixed integer r , Lang and Trotter have conjectured an asymptotic estimate for the number of primes p {600} x such that the trace of Frobenius a p ( E ) = r . Using similar heuristic reasoning, Koblitz has conjectured an asymptotic estimate for the number of primes p {600} x such that the order of the group of points of E over the finite field [Special characters omitted.] is also prime. These estimates have been proven correct for elliptic curves "on average"; however, beyond this the conjectures both remain open. In this thesis, we combine the condition of Lang and Trotter with that of Koblitz to conjecture an asymptotic for the number of primes p {600} x such that both

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Porter, Jeremy Graham
Pagination:vii, 68 leaves : ill. ; 29 cm.
Institution:Concordia University
Degree Name:M. Sc.
Program:Mathematics
Date:2009
Thesis Supervisor(s):David, C
ID Code:976527
Deposited By: Concordia University Library
Deposited On:22 Jan 2013 16:27
Last Modified:18 Jan 2018 17:42
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