Reciprocity laws : from Euler to Eisenstein

Author(s)

• Lemmermeyer, Franz

Bibliographic Information

Reciprocity laws : from Euler to Eisenstein

Franz Lemmermeyer

（Springer monographs in mathematics）

Springer, c2010

• : pbk

Other Title

Reciprocity laws

Note

Includes bibliographical references (p. [419]-471) and indexes

Description and Table of Contents

Description

This book covers 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 be of interest to readers interested in the history of reciprocity laws or in the current research in this area.

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.- A. Dramatis Personae.- B. Chronology of Proofs.- C. Some Open Problems.- References.- Author Index.

by "Nielsen BookData"

• NCID: BB08388349
• ISBN:
  • 9783642086281
• LCCN: 00026905
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Berlin
• Pages/Volumes: xix, 487 p.
• Size: 23 cm
• Classification:
  • DC22 : 512.74
• Subject Headings:
  • LCSH : Reciprocity theorems
  • LCSH : Algebraic number theory
• Parent Bibliography ID:
  • BA3386797X