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The Quadratic Reciprocity Law

A Collection of Classical Proofs

Authors: Baumgart, Oswald

  • Presents detailed descriptions of many proofs of the quadratic reciprocity law
  • Compares and highlights the proofs’ similarities and differences
  • Features a list of all known proofs of the quadratic reciprocity law
  • Offers historical notes on the development of number theory
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eBook 59,49 €
price for Spain (gross)
  • ISBN 978-3-319-16283-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 72,79 €
price for Spain (gross)
  • ISBN 978-3-319-16282-9
  • 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
Softcover 72,79 €
price for Spain (gross)
  • ISBN 978-3-319-36778-1
  • 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 is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise”), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart’s comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix.

This book will appeal to all readers interested in elementary number theory and the history of number theory.

About the authors

Franz Lemmermeyer received his Ph.D. from Heidelberg University and has worked at Universities in California and Turkey. He is now teaching mathematics at the Gymnasium St. Gertrudis in Ellwangen, Germany.

Reviews

“Baumgart collected and analyzed existing proofs of QRL in his 1885 thesis, translated here into English for the first time. … Summing Up: Recommended.” (D. V. Feldman, Choice, Vol. 53 (5), January, 2016)

“The book has an excellent comparative discussion of many proofs along with historic notes and comments by translator. It contains a vast list of references that are updated. … This excellent book is a necessary one for any number theorist. Every student in the field can find a lot of virgin ideas for further research as well. This book should be a good resource for mathematics historian as well.” (Manouchehr Misaghian, zbMATH 1338.11003, 2016)

“The book under review provides an English translation by Franz Lemmermeyer, who is an expert in both the history of mathematics and also in algebraic number theory, of this highly remarkable thesis. In particular, the many valuable comments of the translator make the reading a pleasure and accessible to mathematicians not trained in studying the older literature.” (Jörn Steuding, London Mathematical Society Newsletter, newsletter.lms.ac.uk, November, 2015)

“The editor has provided double service: he offers English-speakers access to Baumgart’s account and provides a summary of what has happened since then. The result is a very useful book.” (Fernando Q. Gouvêa, MAA Reviews, June, 2015)


Table of contents (15 chapters)

  • From Fermat to Legendre

    Baumgart, Oswald

    Pages 3-6

    Preview Buy Chapter 30,19 €
  • Gauss’s Proof by Mathematical Induction

    Baumgart, Oswald

    Pages 7-13

    Preview Buy Chapter 30,19 €
  • Proof by Reduction

    Baumgart, Oswald

    Pages 15-39

    Preview Buy Chapter 30,19 €
  • Eisenstein’s Proof Using Complex Analysis

    Baumgart, Oswald

    Pages 41-44

    Preview Buy Chapter 30,19 €
  • Proofs Using Results from Cyclotomy

    Baumgart, Oswald

    Pages 45-62

    Preview Buy Chapter 30,19 €

Buy this book

eBook 59,49 €
price for Spain (gross)
  • ISBN 978-3-319-16283-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 72,79 €
price for Spain (gross)
  • ISBN 978-3-319-16282-9
  • 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
Softcover 72,79 €
price for Spain (gross)
  • ISBN 978-3-319-36778-1
  • 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
The Quadratic Reciprocity Law
Book Subtitle
A Collection of Classical Proofs
Authors
Translated by
Lemmermeyer, F.
Copyright
2015
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-16283-6
DOI
10.1007/978-3-319-16283-6
Hardcover ISBN
978-3-319-16282-9
Softcover ISBN
978-3-319-36778-1
Edition Number
1
Number of Pages
XIV, 172
Number of Illustrations and Tables
1 b/w illustrations
Topics