ERA

Download the full-sized PDF of Heegner Points, Hilbert's Twelfth Problem, and the Birch and Swinnerton-Dyer ConjectureDownload the full-sized PDF

Analytics

Share

Permanent link (DOI): https://doi.org/10.7939/R38P5VJ4K

Download

Export to: EndNote  |  Zotero  |  Mendeley

Communities

This file is in the following communities:

Graduate Studies and Research, Faculty of

Collections

This file is in the following collections:

Theses and Dissertations

Heegner Points, Hilbert's Twelfth Problem, and the Birch and Swinnerton-Dyer Conjecture Open Access

Descriptions

Other title
Subject/Keyword
Heegner Points
Number Theory
Modular Forms
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Kostiuk, Jordan Allan
Supervisor and department
Doran, Charles (Mathematical and Statistical Sciences)
Examining committee member and department
Kuttler, Jochen (Mathematical and Statistical Sciences)
Lewis, James (Mathematical and Statistical Sciences)
Doran, Charles (Mathematical and Statistical Sciences)
Gannon, Terry (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2013-08-29T22:02:36Z
Graduation date
2013-11
Degree
Master of Science
Degree level
Master's
Abstract
Heegner points on modular curves play a key role in the solution of Hilbert’s twelfth problem for qua- dratic imaginary fields, as well as the proof of the Birch and Swinnerton-Dyer conjecture for the case ords=1 L(E, s) ≤ 1. The relationship between Heegner points and Hilbert’s twelfth is classically described by the j-function; we supply evidence that suggests that this relationship is one that transcends the j-function and should be able to be recast in terms of other suitable modular functions. The proof of the Birch and Swinnerton-Dyer conjecture for the case ords=1 L(E, s) ≤ 1 is examined and made concrete by using sage to illustrate, very explicitly, the role played by the Heegner points. Both of these results suggest a deep connection between geometry and arithmetic that we hope to see in other contexts.
Language
English
DOI
doi:10.7939/R38P5VJ4K
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication

File Details

Date Uploaded
Date Modified
2014-04-30T23:45:49.337+00:00
Audit Status
Audits have not yet been run on this file.
Characterization
File format: pdf (Portable Document Format)
Mime type: application/pdf
File size: 1190819
Last modified: 2015:10:12 14:10:38-06:00
Filename: Kostiuk_Jordan_Summer2013.pdf
Original checksum: dff31a1d690fcb3fd0f8996c9b78ffd0
Well formed: true
Valid: true
File title: pdf
Page count: 61
Activity of users you follow
User Activity Date