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Reciprocity Laws

From Euler to Eisenstein

  • Authors
  • Franz Lemmermeyer

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Franz Lemmermeyer
    Pages 1-42
  3. Franz Lemmermeyer
    Pages 43-78
  4. Franz Lemmermeyer
    Pages 79-110
  5. Franz Lemmermeyer
    Pages 111-152
  6. Franz Lemmermeyer
    Pages 153-183
  7. Franz Lemmermeyer
    Pages 185-207
  8. Franz Lemmermeyer
    Pages 209-233
  9. Franz Lemmermeyer
    Pages 235-288
  10. Franz Lemmermeyer
    Pages 289-316
  11. Franz Lemmermeyer
    Pages 317-356
  12. Franz Lemmermeyer
    Pages 357-410
  13. Back Matter
    Pages 411-489

About this book

Introduction

This book is about the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number theory and Galois theory will find detailed discussions of the reciprocity laws for quadratic, cubic, quartic, sextic and octic residues, rational reciprocity laws, and Eisensteins reciprocity law. An extensive bibliography will particularly appeal to readers interested in the history of reciprocity laws or in the current research in this area.

Keywords

Algebra Elliptic functions Gaus and Jacobi sums Reciprocity Laws Strickelberg's Theorem Zeta functions number theory

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-12893-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08628-1
  • Online ISBN 978-3-662-12893-0
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site