---

＜電子ブック＞
Quadratic Residues and Non-Residues : Selected Topics / by Steve Wright
(Lecture Notes in Mathematics. ISSN:16179692 ; 2171)

版	1st ed. 2016.
出版者	Cham : Springer International Publishing : Imprint: Springer
出版年	2016
大きさ	XIII, 292 p. 20 illus : online resource
著者標目	*Wright, Steve author SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Commutative algebra LCSH:Commutative rings LCSH:Algebraic fields LCSH:Polynomials LCSH:Convex geometry  LCSH:Discrete geometry LCSH:Fourier analysis FREE:Number Theory FREE:Commutative Rings and Algebras FREE:Field Theory and Polynomials FREE:Convex and Discrete Geometry FREE:Fourier Analysis
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-319-45955-4

 類似資料