Quadratic residues and non-residues : selected topics

• 作者： Wright, Steve, author.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • Lecture notes in mathematics ;
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Lecture notes in mathematics,2171
• 主題： Congruences and residues. , Number theory. , Mathematics. , Number Theory. , Commutative Rings and Algebras. , Field Theory and Polynomials. , Convex and Discrete Geometry. , Fourier Analysis.
• ISBN： 9783319459554 (electronic bk.) 、 9783319459547 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 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.
• More
• 摘要註: 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.
• 讀者標籤：

  需登入
• 引用連結：

  Copy Link
• 目前引用數
• Share: