A classical introduction to modern number theory

書誌事項

A classical introduction to modern number theory

Kenneth Ireland, Michael Rosen

(Graduate texts in mathematics, 84)

Springer, 2003

2nd ed

  • pbk

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注記

2nd corr. printing, 1992--Pref

5th corr. printing, 1998--Pref

"Reprinted in China by Beijing World Publishing Corporation, 2003"--T.p. verso

Includes bibliographical references and index

内容説明・目次

内容説明

This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.

目次

1: Unique Factorization. 2: Applications of Unique Factorization. 3: Congruence. 4: The Structure of U. 5: Quadratic Reciprocity. 6: Quadratic Gauss Sums. 7: Finite Fields. 8: Gauss and Jacobi Sums. 9: Cubic and Biquadratic Reciprocity. 10: Equations over Finite Fields. 11: The Zeta Function. 12: Algebraic Number Theory. 13: Quadratic and Cyclotomic Fields. 14: The Stickelberger Relation and the Eisenstein Reciprocity Law. 15: Bernoulli Numbers. 16: Dirichlet L-functions. 17: Diophantine Equations. 18: Elliptic Curves. 19: The Mordell-Weil Theorem. 20: New Progress in Arithmetic Geometry.

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詳細情報

  • NII書誌ID(NCID)
    BD06105222
  • ISBN
    • 9781441930941
  • 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
    xiv, 389 p.
  • 大きさ
    23 cm
  • 分類
  • 件名
  • 親書誌ID
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