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Quadratic residues and non-residues ...

Wright, Steve

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Quadratic residues and non-residues : = selected topics /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Quadratic residues and non-residues :/ SteveWright.
其他題名:	selected topics /
作者:	Wright, Steve
出版者:	[Cham. Switzerland :Springer, : 2016.,
面頁冊數:	xiii, 292 p. :ill. ;24 cm.
標題:	Congruences and residues. -
ISBN:	9783319459547
ISSN:	0075-8434

Quadratic residues and non-residues : = selected topics /
Wright, Steve

Quadratic residues and non-residues :selected topics /SteveWright. - [Cham. Switzerland :Springer,2016. - xiii, 292 p. :ill. ;24 cm. - Lecture notes in mathematics,21710075-8434 ;. - Lecture notes in mathematics (Springer-Verlag) ;2171..

Includes bibliographical references (p. 285-287) and index.

This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some ofthe fundamental methods employed in modern elementary, algebraic,and analytic number theory. The first three chapters present somebasic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet's Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.

ISBN: 9783319459547EUR44.99

ISSN: 0075-8434

LCCN: 2016956697Subjects--Topical Terms:

661653
Congruences and residues.

LC Class. No.: QA242

Dewey Class. No.: 513.6

Quadratic residues and non-residues : = selected topics /
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245 1 0 $a Quadratic residues and non-residues : $b selected topics / $c SteveWright.
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300 $a xiii, 292 p. : $b ill. ; $c 24 cm.
490 1 0 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2171
504 $a Includes bibliographical references (p. 285-287) and index.
520 # $a This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some ofthe fundamental methods employed in modern elementary, algebraic,and analytic number theory. The first three chapters present somebasic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet's Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.
650 # 0 $a Congruences and residues. $3 661653
650 # 0 $a Number theory. $3 515832
830 0 $a Lecture notes in mathematics (Springer-Verlag) ; $v 2171. $3 3166128