Synopses & Reviews
This book provides a brisk, thorough treatment of the foundations of algebraic number theory on which it builds to introduce more advanced topics. Throughout, the authors emphasize the systematic development of techniques for the explicit calculation of the basic invariants such as rings of integers, class groups, and units, combining at each stage theory with explicit computations.
Review
"...an excellent contribution to the long list of books presenting the main results of algebraic number theory. It is useful for anyone who is learning or teaching this branch of mathematics." J. Browkin, Mathematical Reviews
Synopsis
Here is a thorough treatment of the foundations of algebraic number theory which is built on to introduce more advanced ideas. The systematic development of techniques for the explicit calculation of the basic invariants is emphasised throughout. They combine theory with explicit computations and applications, giving motivation in terms of classical number-theoretic problems.
Synopsis
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. 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. 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.
Synopsis
The systematic development of techniques for the explicit calculation of the basic invariants such as rings of integers, class groups, and units, is emphasized throughout this introduction to the foundations of algebraic number theory.
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.