A Classical Introduction to Modern Number Theory: v. 84 (Graduate Texts in Mathematics v. 84 2nd ed. 1990. Corr. 5th printing 1998)

A Classical Introduction to Modern Number Theory: v. 84 (Graduate Texts in Mathematics v. 84 2nd ed. 1990. Corr. 5th printing 1998)

By: Kenneth F. Ireland (author), Michael Rosen (author)Paperback

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Description

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.

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Contents

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.

Product Details

  • publication date: 07/09/1990
  • ISBN13: 9780387973296
  • Format: Paperback, Hardback
  • Number Of Pages: 408
  • ID: 9780387973296
  • weight: 817
  • ISBN10: 038797329X
  • edition: 2nd ed. 1990. Corr. 5th printing 1998

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