A brief guide to algebraic number theory / H.P.F. Swinnerton-Dyer.

Format:

Book

Author/Creator:

Swinnerton-Dyer, H. P. F.

Series:

London Mathematical Society student texts ; 50.

London Mathematical Society student texts ; 50

Language:

English

Subjects (All):

Algebraic number theory.

Physical Description:

ix, 146 pages ; 24 cm.

Place of Publication:

Cambridge : Cambridge University Press, 2001.

Summary:

Broad graduate-level account of Algebraic Number Theory, including exercises, by a world-renowned author.

Contents:

1 Numbers and Ideals 1

1 The ring of integers 1

2 Ideals and factorization 9

3 Embedding in the complex numbers 18

4 Change of fields 23

5 Normal extensions 26

2 Valuations 31

6 Valuations and completions 31

7 Field extensions and ramification 40

8 The Different 43

9 Ideles and Adeles 48

3 Special fields 55

10 Quadratic fields 55

11 Pure cubic fields 62

12 Biquadratic fields 63

13 Cyclotomic fields 65

13.1 Class numbers of cyclotomic fields 68

13.2 Fermat's Last Theorem 73

4 Analytic methods 79

14 Zeta functions and L-series 79

15 Analytic continuation and the functional equation 84

16 Density theorems 94

5 Class Field Theory 98

17 The classical theory 98

18 Chevalley's reformulation 103

19 Reciprocity theorems 106

20 The Kronecker-Weber Theorem 112

A1 Prerequisites 117

A1.1 Finitely generated abelian groups and lattices 117

A1.2 Norms and Traces 121

A1.3 Haar measure 122

A2.1 Characters and duality 125

A2.2 Fourier transforms 128

A2.3 Galois theory for infinite extensions 132.

Notes:

Includes bibliographical references (pages 143-144) and index.

ISBN:

052180292X

0521004233

OCLC:

46448263