Distribution of Selmer Groups of Quadratic Twists of a Family of Elliptic Curves
Xiong, Maosheng
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/86893
Description
Title
Distribution of Selmer Groups of Quadratic Twists of a Family of Elliptic Curves
Author(s)
Xiong, Maosheng
Issue Date
2007
Doctoral Committee Chair(s)
Zaharescu, Alexandru
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
