Algebraic Number Theory

Name: Algebraic Number Theory
Price: 31.2 USD
Availability: InStock
ISBN: 9780521438346

ISBN-10: 0521438349

ISBN-13: 9780521438346

Edition: N/A

Authors: A. Frohlich, M. J. Taylor, B. Bollobas, W. Fulton, A. Katok

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Description:

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…

Book details

List price: $92.99
Publisher: Cambridge University Press
Publication date: 2/4/1993
Binding: Paperback
Pages: 372
Size: 6.25" wide x 9.00" long x 0.75" tall
Weight: 1.144
Language: English



Preface


Notation


Introduction



Algebraic Foundations



Fields and Algebras



Integrality and Noetherian properties



Dedekind Domains



Algebraic Theory



Valuations and absolute values



Completions



Module theory over a Dedekind domain



Extensions



Decomposition and ramification



Discriminants and differents



Non-ramified and tamely ramified extensions



Ramification in Galois extensions



Classgroups and Units



Elementary results



Lattices in Euclidean space



Classgroups



Units



Fields of low degree



Quadratic fields



Biquadratic fields



Cubic and sextic fields



Cyclotomic Fields



Basic theory



Characters



Quadratic fields revisited



Gauss sums



Elliptic curves



Diophantine Equations



Fermat's last theorem



Quadratic forms



Cubic equations



L-functions



Dirichlet series



The Dedekind zeta-function



Dirichlet L-functions



Primes in an arithmetic progression



Evaluation of L(1, x) and explicit class number formulae for cyclotomic fields



Quadratic fields, yet again



Brauer relations



Characters of Finite Abelian Groups


Exercises


Suggested Further Reading


Glossary of Theorems


Index