Overview

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.

Full Product Details

Author:   Steve Wright
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   1st ed. 2016
Volume:   2171
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   4.686kg
ISBN:  

9783319459547

ISBN 10:   3319459546
Pages:   292
Publication Date:   15 November 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

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.

Reviews

Author Information

After earning degrees in mathematics from Western Kentucky University and Indiana University, the author joined the faculty at Oakland University, where he is now Professor of Mathematics in the Department of Mathematics and Statistics. He currently occupies his time studying number theory.

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions