## ＜電子ブック＞Quadratic Residues and Non-Residues : Selected Topics

責任表示 by Steve Wright Wright, Steve SpringerLink (Online service) English (英語) Springer International Publishing Imprint: Springer 2016- Cham, Germany シリーズ Lecture Notes in Mathematics ; 2171 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. Chapter 1. Introduction: Solving the General Quadratic Congruence Modulo a PrimeChapter 2. Basic FactsChapter 3. Gauss' Theorema Aureum: the Law of Quadratic ReciprocityChapter 4. Four Interesting Applications of Quadratic ReciprocityChapter 5. The Zeta Function of an Algebraic Number Field and Some ApplicationsChapter 6. Elementary ProofsChapter 7. Dirichlet L-functions and the Distribution of Quadratic ResiduesChapter 8. Dirichlet's Class-Number FormulaChapter 9. Quadratic Residues and Non-residues in Arithmetic ProgressionChapter 10. Are quadratic residues randomly distributed?Bibliography. http://hdl.handle.net/2324/1001617169 Full text available from SpringerLINK ebooks - Mathematics and Statistics (2016)

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レコードID 1793805 QA241-247.5 512.7 Mathematics. Commutative algebra. Commutative rings. Algebra. Field theory (Physics). Fourier analysis. Convex geometry. Discrete geometry. Number theory. Mathematics. Number Theory. Commutative Rings and Algebras. Field Theory and Polynomials. Convex and Discrete Geometry. Fourier Analysis. ssj0001762829 9783319459547[3319459546](print) 9783319459554[3319459554] 2017.03.07 2017.11.26