Fearnley, Jack (1996) The fundamental critical points of modular elliptic curves. Masters thesis, Concordia University.
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)|
|Pagination:||v, 100 leaves : ill. ; 29 cm.|
|Degree Name:||Theses (M.Sc.)|
|Program:||Mathematics and Statistics|
|Thesis Supervisor(s):||Kisilevsky, H|
|Deposited By:||Concordia University Libraries|
|Deposited On:||27 Aug 2009 13:09|
|Last Modified:||08 Dec 2010 10:12|
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