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The Quadratic Reciprocity Law

A Collection of Classical Proofs

  • Authors
  • Oswald Baumgart

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Presentation of the Proofs of the Quadratic Reciprocity Law

    1. Front Matter
      Pages 1-1
    2. Oswald Baumgart
      Pages 3-6
    3. Oswald Baumgart
      Pages 7-13
    4. Oswald Baumgart
      Pages 15-39
    5. Oswald Baumgart
      Pages 41-44
    6. Oswald Baumgart
      Pages 45-62
    7. Oswald Baumgart
      Pages 63-69
  3. Comparative Presentation of the Principles on Which the Proofs of the Quadratic Reciprocity Law Are Based

    1. Front Matter
      Pages 83-83
    2. Oswald Baumgart
      Pages 85-88
    3. Oswald Baumgart
      Pages 89-105
    4. Oswald Baumgart
      Pages 107-109
    5. Oswald Baumgart
      Pages 111-124
    6. Oswald Baumgart
      Pages 125-126
    7. Oswald Baumgart
      Pages 127-130
    8. Oswald Baumgart
      Pages 131-161
  4. Back Matter
    Pages 163-172

About this book

Introduction

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.

Keywords

Legendre symbols cyclotomy quadratic Gauss sums quadratic reciprocity law quadratic residues

Bibliographic information