Algebraic Number Theory

A graduate text providing a brisk, thorough treatment of the foundations of algebraic number theory.

A. Fröhlich (Author), M. J. Taylor (Author)

9780521438346, Cambridge University Press

Paperback, published 4 February 1993

372 pages, 5 b/w illus.
22.8 x 15.2 x 2.1 cm, 0.6 kg

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

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.

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.

Subject Areas: Number theory [PBH]