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  • © 2016

Quadratic Residues and Non-Residues

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  • 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

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

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  • ISBN: 978-3-319-45955-4
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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
  2. Basic Facts

    • Steve Wright
    Pages 9-19
  3. Elementary Proofs

    • Steve Wright
    Pages 151-160
  4. Dirichlet’s Class-Number Formula

    • Steve Wright
    Pages 203-226
  5. Back Matter

    Pages 285-294

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.

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

  • Department of Mathematics and Statistics, Oakland University, Rochester, USA

    Steve Wright

About the author

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

Buying options

eBook
USD 19.99 USD 44.99
56% discount Price excludes VAT (USA)
  • ISBN: 978-3-319-45955-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 29.99 USD 59.99
50% discount Price excludes VAT (USA)