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＜電子ブック＞
Reciprocity Laws : From Euler to Eisenstein / by Franz Lemmermeyer
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2000.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2000
本文言語	英語
大きさ	XX, 492 p : online resource
著者標目	*Lemmermeyer, Franz author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Number theory FREE:Algebra FREE:Number Theory
一般注記	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 This book is about 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 particularly appeal to readers interested in the history of reciprocity laws or in the current research in this area HTTP:URL=https://doi.org/10.1007/978-3-662-12893-0

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