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Reciprocity Laws

From Euler to Eisenstein

  • Book
  • © 2000

Overview

Authors:
  1. Franz Lemmermeyer
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Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xix
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  2. The Genesis of Quadratic Reciprocity

    • Franz Lemmermeyer
    Pages 1-42

  3. Quadratic Number Fields

    • Franz Lemmermeyer
    Pages 43-78

  4. Cyclotomic Number Fields

    • Franz Lemmermeyer
    Pages 79-110

  5. Power Residues and Gauss Sums

    • Franz Lemmermeyer
    Pages 111-152

  6. Rational Reciprocity Laws

    • Franz Lemmermeyer
    Pages 153-183

  7. Quartic Reciprocity

    • Franz Lemmermeyer
    Pages 185-207

  8. Cubic Reciprocity

    • Franz Lemmermeyer
    Pages 209-233

  9. Eisenstein’s Analytic Proofs

    • Franz Lemmermeyer
    Pages 235-288

  10. Octic Reciprocity

    • Franz Lemmermeyer
    Pages 289-316

  11. Gauss’s Last Entry

    • Franz Lemmermeyer
    Pages 317-356

  12. Eisenstein Reciprocity

    • Franz Lemmermeyer
    Pages 357-410

  13. Back Matter

    Pages 411-489
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Reciprocity Laws

  • Book Subtitle: From Euler to Eisenstein

  • Authors: Franz Lemmermeyer

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-12893-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2000

  • Hardcover ISBN: 978-3-540-66957-9Published: 06 May 2000

  • Softcover ISBN: 978-3-642-08628-1Published: 03 December 2010

  • eBook ISBN: 978-3-662-12893-0Published: 14 March 2013

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XX, 492

  • Topics: Algebra, Number Theory

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