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Algebraic Number Theory

Algebraic Number Theory

textbook

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: February 1993
  • availability: Available
  • format: Paperback
  • isbn: 9780521438346

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About the Authors
  • 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.

    • Eagerly awaited in the maths community
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    Reviews & endorsements

    'It promises to become a classic.' Monatshefte für Mathematik

    '… very nice and carefully written … many excellent exercises…' European Mathematical Society Newsletter

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    Product details

    • Date Published: February 1993
    • format: Paperback
    • isbn: 9780521438346
    • length: 372 pages
    • dimensions: 228 x 152 x 21 mm
    • weight: 0.52kg
    • contains: 5 b/w illus.
    • availability: Available
  • Table of Contents

    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.

  • Authors

    A. Fröhlich, University of London

    M. J. Taylor, University of Manchester Institute of Science and Technology

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