E-Book, Englisch, 492 Seiten, eBook
Lemmermeyer Reciprocity Laws
2000
ISBN: 978-3-662-12893-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
From Euler to Eisenstein
E-Book, Englisch, 492 Seiten, eBook
Reihe: Springer Monographs in Mathematics
ISBN: 978-3-662-12893-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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.
