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Class field theory and the study of N-Fermat primes.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Class field theory and the study of N-Fermat primes./
Author:	Kobin, Andrew.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2015,
Description:	215 p.
Notes:	Source: Masters Abstracts International, Volume: 77-10.
Contained By:	Masters Abstracts International77-10.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=1593163
ISBN:	9781321894486

Class field theory and the study of N-Fermat primes.
Kobin, Andrew.

Class field theory and the study of N-Fermat primes. - Ann Arbor : ProQuest Dissertations & Theses, 2015 - 215 p.

Source: Masters Abstracts International, Volume: 77-10.

Thesis (M.A.)--Wake Forest University, 2015.

This item must not be sold to any third party vendors.

Most problems in number theory are exceedingly simple to state, yet many continue to elude mathematicians even centuries after they were originally posed. Such a question, "Given a positive integer n, when can a prime number be written in the form x 2 + ny2?", was solved by Cox, and although the statement is elementary, the solution requires the depth and power of class field theory to understand. In our approach to this question, we will explore a variety of topics, including: algebraic number fields; types of class groups and class fields; two density theorems; the main theorems in class field theory; and the theory of quadratic forms. Our discussion will culminate in Theorem 2.11.3, a full characterization of primes of the form x2 + ny2 However, the intrigue doesn't end there. In Chapter 3, we pose the related question: "If p is a prime of the form x2 + ny2, when is y2+nx2 also prime?" This question turns out to be much harder to approach, but we will investigate the symmetric n-Fermat prime question thoroughly.

ISBN: 9781321894486Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Algebra

Class field theory and the study of N-Fermat primes.
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100 1 $a Kobin, Andrew. $3 3692422
245 1 0 $a Class field theory and the study of N-Fermat primes.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2015
300 $a 215 p.
500 $a Source: Masters Abstracts International, Volume: 77-10.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Moore, William F.
502 $a Thesis (M.A.)--Wake Forest University, 2015.
506 $a This item must not be sold to any third party vendors.
520 $a Most problems in number theory are exceedingly simple to state, yet many continue to elude mathematicians even centuries after they were originally posed. Such a question, "Given a positive integer n, when can a prime number be written in the form x 2 + ny2?", was solved by Cox, and although the statement is elementary, the solution requires the depth and power of class field theory to understand. In our approach to this question, we will explore a variety of topics, including: algebraic number fields; types of class groups and class fields; two density theorems; the main theorems in class field theory; and the theory of quadratic forms. Our discussion will culminate in Theorem 2.11.3, a full characterization of primes of the form x2 + ny2 However, the intrigue doesn't end there. In Chapter 3, we pose the related question: "If p is a prime of the form x2 + ny2, when is y2+nx2 also prime?" This question turns out to be much harder to approach, but we will investigate the symmetric n-Fermat prime question thoroughly.
590 $a School code: 0248.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Algebra
653 $a Algebraic number theory
653 $a Class field theory
653 $a Number theory
653 $a Quadratic forms
690 $a 0405
690 $a 0642
710 2 $a Wake Forest University. $b Mathematics. $3 2100957
773 0 $t Masters Abstracts International $g 77-10.
790 $a 0248
791 $a M.A.
792 $a 2015
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=1593163