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

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Class field theory and the study of N-Fermat primes./
作者:	Kobin, Andrew.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2015,
面頁冊數:	215 p.
附註:	Source: Masters Abstracts International, Volume: 77-10.
Contained By:	Masters Abstracts International77-10.
標題:	Mathematics. -
電子資源:	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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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.
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