Primes of the form x[2] + ny[2] : Fermat, class field theory, and complex multiplication

著者

• Cox, David A.

書誌事項

Primes of the form x[2] + ny[2] : Fermat, class field theory, and complex multiplication

David A. Cox

（Pure and applied mathematics）

John Wiley & Sons, c1989

• : pbk

タイトル別名

Primes of the form x2 plus ny2

注記

Includes references (p. 335-341) and index (p. 343-351)

"A Wiley-Interscience publication."

内容説明・目次

内容説明

Provides a general solution to the question of which primes p can be expressed in the form x + ny . Covered first are the special cases considered by Fermat, which involve only quadratic reciprocity and the genus theory of quadratic forms. Further, the book shows how the results of Euler and Gauss can be fully understood only in the context of class field theory. Finally, in order to bring class field theory down to earth, the book explores some of the mignificent formulas of complex multiplication.

目次

• FROM FERMAT TO GAUSS.
• Fermat, Euler and Quadratic Reciprocity.
• Lagrange, Legendre and Quadratic Forms.
• Gauss, Composition and Genera.
• Cubic and Biquadratic Reciprocity.
• CLASS FIELD THEORY.
• The Hilbert Class Field and p = x 2 + ny 2 .
• The Hilbert Class Field and Genus Theory.
• Orders in Imaginary Quadratic Fields.
• Class Fields Theory and the Cebotarev Density Theorem.
• Ring Class Field and p = x 2 + ny 2 .
• COMPLEX MULTIPLICATION.
• Elliptic Functions and Complex Multiplication.
• Modular Functions and Ring Class Fields.
• Modular Functions and Singular j--Invariants.
• The Class Equation.
• Ellpitic Curves.
• References.
• Index.

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詳細情報

• NII書誌ID(NCID): BA32988163
• ISBN:
  • 0471190799
• LCCN: 89005555
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: New York
• ページ数/冊数: xi, 351 p.
• 分類:
  • LCC : QA246
  • DC19 : 512/.72
  • NDC8 : 412.1
• 件名:
  • LCSH : Numbers, Prime
• 親書誌ID:
  • BA00007488