Quadratic Residues and Non-Residues Selected Topics /

• Main Author: Wright, Steve (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Lecture Notes in Mathematics, 2171
• Subjects: Mathematics.; Commutative algebra.; Commutative rings.; Algebra.; Field theory (Physics).; Fourier analysis.; Convex geometry.; Discrete geometry.; Number theory.; Number Theory.; Commutative Rings and Algebras.; Field Theory and Polynomials.; Convex and Discrete Geometry.; Fourier Analysis.

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...

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.