Algebraic Number Theory

By: A. Frohlich, M. J. Taylor

Write A Review

Paperback | 5 April 1993

At a Glance

Paperback
372 Pages

Dimensions(cm)
23.0 x 15.1 x 2.3

Paperback

RRP $117.95

$108.95

or 4 interest-free payments of $27.24 with

or

Aims to ship in 7 to 10 business days

When will this arrive by?
Enter delivery postcode to estimate

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.

Industry Reviews

'It promises to become a classic.' Monatshefte fur Mathematik '... very nice and carefully written ... many excellent exercises...' European Mathematical Society Newsletter

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Number Theory

Sum Stories Equations and Their Origins : Equations and Their Origins - Robin Wilson

$197.25

10%
OFF

Nankai Symposium on Mathematical Dialogues : Celebrating the 110th anniversary of the birth of Prof. S.-S. Chern - Yang-Hui He

$24.75

Causality

The p-adic Theory

Hardcover

$347.88

$SEL PROB VIETNAMESE MATH'L..(V5) : Mathematical Olympiad - LE HAI CHAU & LE HAI KHOI$

$2ND STEP MATH OLYMPIAD PROB(V7) : Mathematical Olympiad - DEREK HOLTON$

2ND STEP MATH OLYMPIAD PROB(V7)

Mathematical Olympiad

Paperback

RRP $62.70

$48.95

22%
OFF

BOOK OF NUMBERS, THE - TIANXIN CAI & JIU DING

$131.40

17%
OFF

Exponential Sums, Hypergeometric Sheaves and Monodromy Groups : Annals of Mathematics Studies - Nicholas M. Katz

$80.25

14%
OFF

Essays in Classical Number Theory : Cambridge Studies in Advanced Mathematics - Yoichi Motohashi

$Love and Math : The Heart of Hidden Reality - Edward Frenkel$

Love and Math

The Heart of Hidden Reality

Paperback

RRP $34.99

$28.50

19%
OFF

Preface	p. ix
Notation	p. xiii
Introduction	p. 1
Algebraic Foundations	p. 8
Fields and Algebras	p. 8
Integrality and Noetherian properties	p. 26
Dedekind Domains	p. 35
Algebraic Theory	p. 35
Valuations and absolute values	p. 58
Completions	p. 70
Module theory over a Dedekind domain	p. 87
Extensions	p. 102
Decomposition and ramification	p. 102
Discriminants and differents	p. 120
Non-ramified and tamely ramified extensions	p. 132
Ramification in Galois extensions	p. 142
Classgroups and Units	p. 152
Elementary results	p. 152
Lattices in Euclidean space	p. 156
Classgroups	p. 164
Units	p. 168
Fields of low degree	p. 175
Quadratic fields	p. 175
Biquadratic fields	p. 193
Cubic and sextic fields	p. 198
Cyclotomic Fields	p. 205
Basic theory	p. 205
Characters	p. 213
Quadratic fields revisited	p. 220
Gauss sums	p. 231
Elliptic curves	p. 241
Diophantine Equations	p. 251
Fermat's last theorem	p. 251
Quadratic forms	p. 254
Cubic equations	p. 269
L-functions	p. 277
Dirichlet series	p. 277
The Dedekind zeta-function	p. 283
Dirichlet L-functions	p. 295
Primes in an arithmetic progression	p. 297
Evaluation of L(1, x) and explicit class number formulae for cyclotomic fields	p. 299
Quadratic fields, yet again	p. 306
Brauer relations	p. 309
Characters of Finite Abelian Groups	p. 327
Exercises	p. 335
Suggested Further Reading	p. 349
Glossary of Theorems	p. 352
Index	p. 353
Table of Contents provided by Syndetics. All Rights Reserved.

Algebraic Number Theory

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Number Theory

Sum Stories Equations and Their Origins

Equations and Their Origins

Primes as Sums of Fibonacci Numbers

Nankai Symposium on Mathematical Dialogues

Celebrating the 110th anniversary of the birth of Prof. S.-S. Chern

Introduction to Modern Cryptography

Fourth Edition

Exponential Sums, Hypergeometric Sheaves, and Monodromy Groups

Annals of Mathematics Studies

Srinivasa Ramanujan

His Life, Legacy, and Mathematical Influence

The Tiger That Isn't

Seeing Through a World of Numbers

Causality

The p-adic Theory

SEL PROB VIETNAMESE MATH'L..(V5)

Mathematical Olympiad

PROBLEMS OF NUMBER THEORY IN MATHEMATICAL COMPETITIONS

Mathematical Olympiad

2ND STEP MATH OLYMPIAD PROB(V7)

Mathematical Olympiad

BOOK OF NUMBERS, THE

Algebraic Operads

An Algorithmic Companion

Exponential Sums, Hypergeometric Sheaves and Monodromy Groups

Annals of Mathematics Studies

A Mathematical Tour

Essays in Classical Number Theory

Cambridge Studies in Advanced Mathematics

Chord Transformations in Higher-Dimensional Networks

Love and Math

The Heart of Hidden Reality

Analytic Number Theory and Algebraic Asymptotic Analysis

Computational and Algorithmic Problems in Finite Fields

NATO Asi Series. Series E, Applied Sciences

Number Theory and Discrete Mathematics

Trends in Mathematics

Number Theory

New York Seminar 2003

Applications of Fibonacci Numbers

Volume 8

Groups, Combinatorics and Geometry

This product is categorised by