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The fundamental critical points of modular elliptic curves

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The fundamental critical points of modular elliptic curves

Fearnley, Jack (1996) The fundamental critical points of modular elliptic curves. Masters thesis, Concordia University.

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Abstract

In their paper, "Arithmetic of Weil Curves", Mazur and Swinnerton-Dyer prove that the number of fundamental critical points of the normalized weight two modular form associated with an elliptic curve is an upper bound on the analytic rank of the curve. Their calculation of this quantity for all elliptic curves of conductor less than 424 confirmed that, with only 16 exceptions, the bound is sharp. It is the intention of this thesis to compute the number of fundamental critical points for all curves of conductor less than 4000.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Fearnley, Jack
Pagination:v, 100 leaves : ill. ; 29 cm.
Institution:Concordia University
Degree Name:Theses (M.Sc.)
Program:Mathematics and Statistics
Date:1996
Thesis Supervisor(s):Kisilevsky, H
ID Code:125
Deposited By:Concordia University Libraries
Deposited On:27 Aug 2009 13:09
Last Modified:08 Dec 2010 10:12
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