書誌事項

Algebraic number theory

A. Fröhlich, M.J. Taylor

(Cambridge studies in advanced mathematics, 27)

Cambridge University Press, 1991

大学図書館所蔵 件 / 73

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注記

Bibliography: p. [349]-351

Includes index

内容説明・目次

内容説明

This book originates from graduate courses given in Cambridge and London. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas. Throughout, the authors emphasise the systematic development of techniques for the explicit calculation of the basic invariants, such as rings of integers, class groups, and units. Moreover they combine, at each stage of development, theory with explicit computations and applications, and provide motivation in terms of classical number-theoretic problems. A number of special topics are included that can be treated at this level but can usually only be found in research monographs or original papers, for instance: module theory of Dedekind domains; tame and wild ramifications; Gauss series and Gauss periods; binary quadratic forms; and Brauer relations. This is the only textbook at this level which combines clean, modern algebraic techniques together with a substantial arithmetic content. It will be indispensable for all practising and would-be algebraic number theorists.

目次

  • Notation
  • Introduction
  • 1. Algebraic foundations
  • 2. Dedekind domains
  • 3. Extensions
  • 4. Classgroups and units
  • 5. Fields of low degree
  • 6. Cyclotomic fields
  • 7. Diophantine equations
  • 8. L-functions
  • Appendices
  • Exercises
  • Glossary of theorems
  • Index.

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詳細情報

  • NII書誌ID(NCID)
    BA13405075
  • ISBN
    • 052136664X
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cambridge
  • ページ数/冊数
    xiv, 355 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
  • 親書誌ID
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