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Quadratic residues and non-residues[electronic resource] :selected topics /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	512.72
書名/作者:	Quadratic residues and non-residues : selected topics // by Steve Wright.
作者:	Wright, Steve.
出版者:	Cham : : Springer International Publishing :, 2016.
面頁冊數:	xiii, 292 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Congruences and residues.
標題:	Number theory.
標題:	Mathematics.
標題:	Number Theory.
標題:	Commutative Rings and Algebras.
標題:	Field Theory and Polynomials.
標題:	Convex and Discrete Geometry.
標題:	Fourier Analysis.
ISBN:	9783319459554
ISBN:	9783319459547
內容註:	Chapter 1. Introduction: Solving the General Quadratic Congruence Modulo a Prime -- Chapter 2. Basic Facts -- Chapter 3. Gauss' Theorema Aureum: the Law of Quadratic Reciprocity -- Chapter 4. Four Interesting Applications of Quadratic Reciprocity -- Chapter 5. The Zeta Function of an Algebraic Number Field and Some Applications -- Chapter 6. Elementary Proofs -- Chapter 7. Dirichlet L-functions and the Distribution of Quadratic Residues -- Chapter 8. Dirichlet's Class-Number Formula -- Chapter 9. Quadratic Residues and Non-residues in Arithmetic Progression -- Chapter 10. Are quadratic residues randomly distributed? -- Bibliography.
摘要、提要註:	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 of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic 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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-45955-4

Quadratic residues and non-residues[electronic resource] :selected topics /
Wright, Steve.

Quadratic residues and non-residuesselected topics /[electronic resource] :by Steve Wright. - Cham :Springer International Publishing :2016. - xiii, 292 p. :ill., digital ;24 cm. - Lecture notes in mathematics,21710075-8434 ;. - Lecture notes in mathematics ;2035..

Chapter 1. Introduction: Solving the General Quadratic Congruence Modulo a Prime -- Chapter 2. Basic Facts -- Chapter 3. Gauss' Theorema Aureum: the Law of Quadratic Reciprocity -- Chapter 4. Four Interesting Applications of Quadratic Reciprocity -- Chapter 5. The Zeta Function of an Algebraic Number Field and Some Applications -- Chapter 6. Elementary Proofs -- Chapter 7. Dirichlet L-functions and the Distribution of Quadratic Residues -- Chapter 8. Dirichlet's Class-Number Formula -- Chapter 9. Quadratic Residues and Non-residues in Arithmetic Progression -- Chapter 10. Are quadratic residues randomly distributed? -- Bibliography.

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 of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic 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: 9783319459554

Standard No.: 10.1007/978-3-319-45955-4doiSubjects--Topical Terms:

673068
Congruences and residues.

LC Class. No.: QA242

Dewey Class. No.: 512.72

Quadratic residues and non-residues[electronic resource] :selected topics /
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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 of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic 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.
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650 2 4 $a Field Theory and Polynomials. $3 467525
650 2 4 $a Convex and Discrete Geometry. $3 470189
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