Reciprocity Laws
From Euler to Eisenstein
Published on 3. December 2010
Book
Paperback/Softback
XX, 492 pages
978-3-642-08628-1 (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
Softcover reprint of hardcover 1st ed. 2000
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XX, 492 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 28 mm
Weight
768 gr
ISBN-13
978-3-642-08628-1 (9783642086281)
DOI
10.1007/978-3-662-12893-0
Schweitzer Classification
Other editions
Additional editions
Book
05/2000
Springer
€149.79
Shipment within 10-15 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.