# Quadratic Residues and Non-Residues

## Selected Topics

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2171)

1. Front Matter
Pages i-xiii
2. Steve Wright
Pages 1-8
3. Steve Wright
Pages 9-19
4. Steve Wright
Pages 21-77
5. Steve Wright
Pages 79-118
6. Steve Wright
Pages 119-150
7. Steve Wright
Pages 151-160
8. Steve Wright
Pages 161-201
9. Steve Wright
Pages 203-226
10. Steve Wright
Pages 227-271
11. Steve Wright
Pages 273-283
12. Back Matter
Pages 285-294

### Introduction

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.

### Keywords

11-XX; 12D05, 13B05, 52C05, 42A16, 42A20 quadratic residues quadratic non-residues law of quadratic reciprocity distribution of quadratic residues quadratic residues in arithmetic progression

#### Authors and affiliations

1. 1.Department of Mathematics and StatisticsOakland UniversityRochesterUSA

#### About the authors

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.

### Bibliographic information

• Book Title Quadratic Residues and Non-Residues
• Book Subtitle Selected Topics
• Authors Steve Wright
• Series Title Lecture Notes in Mathematics
• Series Abbreviated Title Lect.Notes Mathematics
• DOI https://doi.org/10.1007/978-3-319-45955-4
• Copyright Information Springer International Publishing Switzerland 2016
• Publisher Name Springer, Cham
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Softcover ISBN 978-3-319-45954-7
• eBook ISBN 978-3-319-45955-4
• Series ISSN 0075-8434
• Series E-ISSN 1617-9692
• Edition Number 1
• Number of Pages XIII, 292
• Number of Illustrations 20 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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