A brief guide to algebraic number theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2002
|
| Ausgabe: | Reprint. |
| Schriftenreihe: | London Mathematical Society student texts
50 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 146 S. |
| ISBN: | 0521004233 052180292X |
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Datensatz im Suchindex
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| adam_text | Titel: A brief guide to algebraic number theory
Autor: Swinnerton-Dyer, Henry P. F
Jahr: 2002
Contents
Preface page vii
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 84
5 Class Field Theory 98
17 The classical theory 98
18 Chevalley s reformulation 103
v
vi Contents
19 Reciprocity theorems 106
20 The Kronecker-Weber Theorem 112
Appendix 117
Al Prerequisites 117
A 1.1 Finitely generated abelian groups and lattices 117
Al.2 Norms and Traces 121
A1.3 Haar measure 122
A2 Additional topics 124
A2.1 Characters and duality 125
A2.2 Fourier transforms 128
A2.3 Galois theory for infinite extensions 132
Exercises 135
Suggested further reading 143
Index 145
|
| adam_txt |
Titel: A brief guide to algebraic number theory
Autor: Swinnerton-Dyer, Henry P. F
Jahr: 2002
Contents
Preface page vii
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 84
5 Class Field Theory 98
17 The classical theory 98
18 Chevalley's reformulation 103
v
vi Contents
19 Reciprocity theorems 106
20 The Kronecker-Weber Theorem 112
Appendix 117
Al Prerequisites 117
A 1.1 Finitely generated abelian groups and lattices 117
Al.2 Norms and Traces 121
A1.3 Haar measure 122
A2 Additional topics 124
A2.1 Characters and duality 125
A2.2 Fourier transforms 128
A2.3 Galois theory for infinite extensions 132
Exercises 135
Suggested further reading 143
Index 145 |
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| physical | IX, 146 S. |
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| series | London Mathematical Society student texts |
| series2 | London Mathematical Society student texts |
| spelling | Swinnerton-Dyer, Henry P. F. 1927-2018 Verfasser (DE-588)114274185 aut A brief guide to algebraic number theory H. P. F. Swinnerton-Dyer Reprint. Cambridge [u.a.] Cambridge Univ. Press 2002 IX, 146 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society student texts 50 Algebraische Zahlentheorie Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Algebraische Zahlentheorie (DE-588)4001170-7 s DE-604 London Mathematical Society student texts 50 (DE-604)BV000841726 50 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016243661&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Swinnerton-Dyer, Henry P. F. 1927-2018 A brief guide to algebraic number theory London Mathematical Society student texts Algebraische Zahlentheorie Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| subject_GND | (DE-588)4001170-7 (DE-588)4151278-9 |
| title | A brief guide to algebraic number theory |
| title_auth | A brief guide to algebraic number theory |
| title_exact_search | A brief guide to algebraic number theory |
| title_exact_search_txtP | A brief guide to algebraic number theory |
| title_full | A brief guide to algebraic number theory H. P. F. Swinnerton-Dyer |
| title_fullStr | A brief guide to algebraic number theory H. P. F. Swinnerton-Dyer |
| title_full_unstemmed | A brief guide to algebraic number theory H. P. F. Swinnerton-Dyer |
| title_short | A brief guide to algebraic number theory |
| title_sort | a brief guide to algebraic number theory |
| topic | Algebraische Zahlentheorie Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| topic_facet | Algebraische Zahlentheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016243661&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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