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Quadratic Residues and Non-Residues Selected Topics

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 chapt...

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Bibliographic Details
Main Author: Wright, Steve
Format: eBook
Language:English
Published: Cham Springer International Publishing 2016, 2016
Edition:1st ed. 2016
Series:Lecture Notes in Mathematics
Subjects:
Number Theory
Convex And Discrete Geometry
Commutative Algebra
Fourier Analysis
Commutative Rings And Algebras
Convex Geometry 
Algebra
Commutative Rings
Field Theory (physics)
Discrete Geometry
Field Theory And Polynomials
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • 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

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