Algebraic Number Theory - A. Fröhlich, M. J. Taylor

Algebraic Number Theory

Buch | Hardcover
369 Seiten
1991
Cambridge University Press (Verlag)
978-0-521-36664-9 (ISBN)
79,95 inkl. MwSt
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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.
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.

Erscheint lt. Verlag 12.12.1991
Reihe/Serie Cambridge Studies in Advanced Mathematics
Zusatzinfo 5 Line drawings, unspecified
Verlagsort Cambridge
Sprache englisch
Maße 157 x 235 mm
Gewicht 646 g
Themenwelt Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
ISBN-10 0-521-36664-X / 052136664X
ISBN-13 978-0-521-36664-9 / 9780521366649
Zustand Neuware
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