Page 1 |
Save page Remove page | Previous | 1 of 63 | Next |
|
small (250x250 max)
medium (500x500 max)
Large (1000x1000 max)
Extra Large
large ( > 500x500)
Full Resolution
All (PDF)
|
This page
All
|
On the torsion structure of elliptic curves over cubic number fields.
by
Jian Wang
————————————————————————–
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATHEMATICS)
August 2015
Copyright 2015 Jian Wang
Object Description
| Title | On the torsion structure of elliptic curves over cubic number fields |
| Author | Wang, Jian |
| Author email | wang50@usc.edu;blandye@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2015-04-22 |
| Date submitted | 2015-06-25 |
| Date approved | 2015-06-25 |
| Restricted until | 2015-06-25 |
| Date published | 2015-06-25 |
| Advisor (committee chair) | Kamienny, Sheldon |
| Advisor (committee member) |
Guralnick, Robert M. Golubchik, Leana |
| Abstract | Let E be an elliptic curve defined over a number field K. Then its Mordell-Weil group E(K) is finitely generated: E(K)≅ E(K)tor × ℤʳ. In this thesis, I will discuss the cyclic torsion subgroup of elliptic curves over cubic number fields. I obtained complete results in the prime power case and partial results in the composite case. |
| Keyword | elliptic curves; modular curves; torsion; cubic fields |
| Language | English |
| Format (imt) | application/pdf |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Contributing entity | University of Southern California |
| Rights | Wang, Jian |
| Physical access | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@lib.usc.edu |
| Filename | etd-WangJian-3514.pdf |
| Archival file | Volume2/etd-WangJian-3514.pdf |
Description
| Title | Page 1 |
| Repository email | cisadmin@lib.usc.edu |
| Full text | On the torsion structure of elliptic curves over cubic number fields. by Jian Wang ————————————————————————– A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MATHEMATICS) August 2015 Copyright 2015 Jian Wang |
