Distribution of Selmer Groups of Quadratic Twists of a Family of Elliptic Curves

Xiong, Maosheng

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Title:	Distribution of Selmer Groups of Quadratic Twists of a Family of Elliptic Curves
Author(s):	Xiong, Maosheng
Doctoral Committee Chair(s):	Zaharescu, Alexandru
Department / Program:	Mathematics
Discipline:	Mathematics
Degree Granting Institution:	University of Illinois at Urbana-Champaign
Degree:	Ph.D.
Genre:	Dissertation
Subject(s):	Mathematics
Abstract:	As an most interesting example for the elliptic curve E n : y2 = x 3 - n2x, which is closely related with the congruent number problem, we study the distribution of the size of the six Selmer groups arising from the three 2-isogenies and their dual 2-isogenies. We also describe explicit formulas on the size of the six Selmer groups.
Issue Date:	2007
Type:	Text
Language:	English
Description:	62 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007.
URI:	http://hdl.handle.net/2142/86893
Other Identifier(s):	(MiAaPQ)AAI3290437
Date Available in IDEALS:	2015-09-28
Date Deposited:	2007