Reciprocity Laws: From Euler to Eisenstein / Edition 1

Reciprocity Laws: From Euler to Eisenstein / Edition 1

by Franz Lemmermeyer, F. Lemmermeyer
     
 

ISBN-10: 3540669574

ISBN-13: 9783540669579

Pub. Date: 06/08/2000

Publisher: Springer Berlin Heidelberg

This book is about the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gau ss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number theory and Galois theory will find detailed discussio ns of the reciprocity laws for quadratic, cubic, quartic, sextic and o ctic residues,

…  See more details below

Overview

This book is about the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gau ss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number theory and Galois theory will find detailed discussio ns of the reciprocity laws for quadratic, cubic, quartic, sextic and o ctic residues, rational reciprocity laws, and Eisenstein's reciprocity law. An extensive bibliography will be of interest to readers interes ted in the history of reciprocity laws or in the current research in t his area.

Product Details

ISBN-13:
9783540669579
Publisher:
Springer Berlin Heidelberg
Publication date:
06/08/2000
Series:
Springer Monographs in Mathematics Series
Edition description:
2000
Pages:
492
Product dimensions:
1.19(w) x 6.14(h) x 9.21(d)

Table of Contents

1. The Genesis of Quadratic Reciprocity.- 2. Quadratic Number Fields.- 3. Cyclotomic Number Fields.- 4. Power Residues and Gauss Sums.- 5. Rational Reciprocity Laws.- 6. Quartic Reciprocity.- 7. Cubic Reciprocity.- 8. Eisenstein's Analytic Proofs.- 9. Octic Reciprocity.- 10. Gauss's Last Entry.- 11. Eisenstein Reciprocity.- Appendix.- A. Dramatis Personae.- B. Chronology of Proofs.

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >