Franz Lemmermeyer

Reciprocity Laws (eBook, PDF)

From Euler to Eisenstein

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 492
• Erscheinungstermin: 14. März 2013
• Englisch
• ISBN-13: 9783662128930
• Artikelnr.: 53156419

Autorenporträt

Franz Lemmermeyer has worked in algebraic number theory and has published several books on the history of number theory, in particular on reciprocity laws.

Inhaltsangabe

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.