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...
Main Author: | |
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Format: | eBook |
Language: | English |
Published: |
Cham
Springer International Publishing
2016, 2016
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Edition: | 1st ed. 2016 |
Series: | Lecture Notes in Mathematics
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Subjects: | |
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