Home WakeSpace Scholarship › Electronic Theses and Dissertations

Quadratic Forms Representing All Integers Coprime to 3

Electronic Theses and Dissertations

Item Files

Item Details

abstract
Drawing up on the methods developed by Bhargava to prove "The Fifteen Theorem" and expanded by Rouse when handling integer-valued quadratic forms representing odd integers, we show that an integer-valued quadratic form representing all positive integers coprime to 3 up to 290 must represent all positive integers coprime to 3. We further this result by enumerating a list of 31 critical numbers such that representing all numbers on the list guarantees an integer-valued quadratic form represents all positive integers coprime to 3. Finally, we show that no numbers can be removed from this list.
subject
Local Density
Modular Forms
Number Theory
Quadratic Forms
contributor
DeBenedetto, Justin Donald (author)
Rouse, Jeremy (committee chair)
Howards, Hugh N (committee member)
Berenhaut, Kenneth S (committee member)
date
2015-06-23T08:35:57Z (accessioned)
2015-06-23T08:35:57Z (available)
2015 (issued)
degree
Mathematics (discipline)
identifier
http://hdl.handle.net/10339/57168 (uri)
language
en (iso)
publisher
Wake Forest University
title
Quadratic Forms Representing All Integers Coprime to 3
type
Thesis

Usage Statistics

 

If you have any questions, please contact Molly Keener, Director of Digital Initiatives & Scholarly Communication.