Lecture Notes in Mathematics

Quadratic Residues and Non-Residues

Selected Topics

Authors: Wright, Steve

  • Illustrates how the study of quadratic residues led directly to the development of fundamental methods in elementary, algebraic, and analytic number theory
  • Presents in detail seven proofs of the Law of Quadratic Reciprocity, with an emphasis on the six proofs which Gauss published
  • Discusses in some depth the historical development of the study of quadratic residues and non-residues
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eBook 41,64 €
price for Spain (gross)
  • ISBN 978-3-319-45955-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-319-45954-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

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.

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.

Table of contents (10 chapters)

  • Introduction: Solving the General Quadratic Congruence Modulo a Prime

    Wright, Steve

    Pages 1-8

    Preview Buy Chapter 30,19 €
  • Basic Facts

    Wright, Steve

    Pages 9-19

    Preview Buy Chapter 30,19 €
  • Gauss’ Theorema Aureum: The Law of Quadratic Reciprocity

    Wright, Steve

    Pages 21-77

    Preview Buy Chapter 30,19 €
  • Four Interesting Applications of Quadratic Reciprocity

    Wright, Steve

    Pages 79-118

    Preview Buy Chapter 30,19 €
  • The Zeta Function of an Algebraic Number Field and Some Applications

    Wright, Steve

    Pages 119-150

    Preview Buy Chapter 30,19 €

Buy this book

eBook 41,64 €
price for Spain (gross)
  • ISBN 978-3-319-45955-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-319-45954-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Quadratic Residues and Non-Residues
Book Subtitle
Selected Topics
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2171
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-45955-4
DOI
10.1007/978-3-319-45955-4
Softcover ISBN
978-3-319-45954-7
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIII, 292
Number of Illustrations
20 b/w illustrations
Topics