Algebraic number theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1977
|
| Series: | Pure and applied mathematics
41 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 192 S. |
| ISBN: | 0824765400 |
Staff View
MARC
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| 245 | 1 | 0 | |a Algebraic number theory |c Robert L. Long |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface iii
Chapter 1 DEDEKIND DOMAINS AND ALGEBRAIC NUMBER THEORY 1
1. Dedekind Domains 1
2. Extensions of Dedekind Domains 4
3. Algebraic Numbers 5
4. Theory of Ramification in Galois Extensions 7
5. Finitely Generated Modules over a Dedekind Domain 11
Chapter 2 LOCALIZATION AND MODULE INDICES 15
1. Discrete Valuation Rings 15
2. Module Indices 18
3. Eisenstein Polynomials 21
4. The Inequality I e.f. n 23
Exercises 25
Chapter 3 ABSOLUTE VALUES AND COMPLETIONS 27
1. Absolute Values 28
2. Completion 32
3. Extensions 41
Exercises 52
Chapter 4 THE p ADIC FIELDS 57
1. Factorization of Polynomials 57
2. The Multiplicative Structure 60
3. Galois Action 65
Exercises 69
vii
viii CONTENTS
Chapter 5 THE DIFFERENT AND RAMIFICATION 73
1. The Different 74
2. The Discriminant 80
Exercises 82
Chapter 6 CYCLOTOMIC AND ABELIAN EXTENSIONS OF THE RATIONALS 87
1. Algebraic Results 88
2. Dirichlet Characters and Gaussian Sums 98
Exercises 107
Chapter 7 ZETA FUNCTIONS AND L SERIES 111
1. Asymptotic Estimate for the Number of Ideals in an
Ideal Class 112
2. Dirichlet Series 120
3. The Zeta Function of an Algebraic Number Field 123
4. L Functions 126
5. Primes in an Arithmetic Progression 127
6. Abelian Extensions of Q 129
7. Functional Equation 130
Exercises 132
Chapter 8 CLASS NUMBER FORMULAS 135
1. Summation of the L Series 136
2. Quadratic Fields 139
3. Relative Class Number 142
4. Class Numbers of Real Abelian Fields 151
Exercises 157
Chapter 9 ACTION OF THE GROUP RING IN A GALOIS EXTENSION 161
1. Tame Ramification and Projective AG Modules 162
2. Normal Integral Bases for Extensions of p adic Fields 163
3. Tamely Ramified Abelian Extensions of Q 165
4. Leopoldt s Reflection Theorem 167
Exercises 177
CONTENTS ix
Bibliography 183
List of Symbols 187
Index 191
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.74 |
| dewey-search | 512/.74 |
| dewey-sort | 3512 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002252578 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:49Z |
| institution | BVB |
| isbn | 0824765400 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001480189 |
| oclc_num | 3205795 |
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| owner_facet | DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-29T DE-11 DE-188 DE-706 |
| physical | IX, 192 S. |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Long, Robert L. J. 1920- Verfasser (DE-588)119398974 aut Algebraic number theory Robert L. Long New York [u.a.] Dekker 1977 IX, 192 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 41 Algebraïsche getallen gtt Getaltheorie gtt Nombres algébriques, Théorie des Algebraic number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 s DE-604 Zahlentheorie (DE-588)4067277-3 s Pure and applied mathematics 41 (DE-604)BV000001885 41 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001480189&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Long, Robert L. J. 1920- Algebraic number theory Pure and applied mathematics Algebraïsche getallen gtt Getaltheorie gtt Nombres algébriques, Théorie des Algebraic number theory Zahlentheorie (DE-588)4067277-3 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4001170-7 |
| title | Algebraic number theory |
| title_auth | Algebraic number theory |
| title_exact_search | Algebraic number theory |
| title_full | Algebraic number theory Robert L. Long |
| title_fullStr | Algebraic number theory Robert L. Long |
| title_full_unstemmed | Algebraic number theory Robert L. Long |
| title_short | Algebraic number theory |
| title_sort | algebraic number theory |
| topic | Algebraïsche getallen gtt Getaltheorie gtt Nombres algébriques, Théorie des Algebraic number theory Zahlentheorie (DE-588)4067277-3 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| topic_facet | Algebraïsche getallen Getaltheorie Nombres algébriques, Théorie des Algebraic number theory Zahlentheorie Algebraische Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001480189&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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