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Quadratic Residues and Non-Residues

Selected Topics

  • Steve Wright

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

Table of contents

About this book

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

  • Steve Wright
    • 1
  1. 1.Department of Mathematics and StatisticsOakland UniversityRochesterUSA

Bibliographic information

  • 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
  • Print ISBN 978-3-319-45954-7
  • Online ISBN 978-3-319-45955-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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