Reciprocity Laws
From Euler to Eisenstein
Published on 6. May 2000
Book
Hardback
XX, 492 pages
978-3-540-66957-9 (ISBN)
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.
More details
Series
Edition
2000 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XX, 492 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 33 mm
Weight
928 gr
ISBN-13
978-3-540-66957-9 (9783540669579)
DOI
10.1007/978-3-662-12893-0
Schweitzer Classification
Other editions
Additional editions
Book
12/2010
Springer
€149.79
Shipment within 7-9 days
Person
Franz Lemmermeyer hat nach seiner Promotion in Heidelberg und seiner Habilitation in Bonn an Universitäten in den USA und in der Türkei gelehrt, und unterrichtet seit 2007 Mathematik am Gymnasium St. Gertrudis in Ellwangen.
Content
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.