Item Details

title

Quadratic Forms Representing All Integers Coprime to 3

author

DeBenedetto, Justin Donald

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

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

type

Thesis