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Reciprocity Laws Franz Lemmermeyer

Reciprocity Laws By Franz Lemmermeyer

Reciprocity Laws by Franz Lemmermeyer


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Summary

Talks about the development of reciprocity laws, starting from conjectures of Euler. This book discusses the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. It provides discussions of the reciprocity laws for quadratic, cubic, quartic, sextic and octic residues, rational reciprocity laws, and Eisenstein's reciprocity law.

Reciprocity Laws Summary

Reciprocity Laws: From Euler to Eisenstein by Franz Lemmermeyer

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.

Table of Contents

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. Eisensteins Analytic Proofs.- 9. Octic Reciprocity.- 10. Gausss Last Entry.- 11. Eisenstein Reciprocity.- A. Dramatis Personae.- B. Chronology of Proofs.- C. Some Open Problems.- References.- Author Index.

Additional information

NPB9783540669579
9783540669579
3540669574
Reciprocity Laws: From Euler to Eisenstein by Franz Lemmermeyer
New
Hardback
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
2000-05-06
492
N/A
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