Overview
- 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)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (10 chapters)
-
Front Matter
-
Back Matter
Keywords
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.Authors and Affiliations
About the author
Bibliographic Information
Book Title: Quadratic Residues and Non-Residues
Book Subtitle: Selected Topics
Authors: Steve Wright
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-45955-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-45954-7Published: 15 November 2016
eBook ISBN: 978-3-319-45955-4Published: 11 November 2016
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIII, 292
Number of Illustrations: 20 b/w illustrations
Topics: Number Theory, Commutative Rings and Algebras, Field Theory and Polynomials, Convex and Discrete Geometry, Fourier Analysis