Reciprocity laws : from Euler to Eisenstein

著者

• Lemmermeyer, Franz

書誌事項

Reciprocity laws : from Euler to Eisenstein

Franz Lemmermeyer

（Springer monographs in mathematics）

Springer, c2010

• : pbk

タイトル別名

Reciprocity laws

注記

Includes bibliographical references (p. [419]-471) and indexes

内容説明・目次

内容説明

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.

目次

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.

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詳細情報

• NII書誌ID(NCID): BB08388349
• ISBN:
  • 9783642086281
• LCCN: 00026905
• 出版国コード: gw
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Berlin
• ページ数/冊数: xix, 487 p.
• 大きさ: 23 cm
• 分類:
  • DC22 : 512.74
• 件名:
  • LCSH : Reciprocity theorems
  • LCSH : Algebraic number theory
• 親書誌ID:
  • BA3386797X