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.
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Research
Illustrationen
Maße
Höhe: 241 mm
Breite: 160 mm
Dicke: 33 mm
Gewicht
ISBN-13
978-3-540-66957-9 (9783540669579)
DOI
10.1007/978-3-662-12893-0
Schweitzer Klassifikation
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.
