Elementary and analytic theory of algebraic numbers:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer u.a.
1990
|
| Edition: | 2. ed., substantially rev. and extended |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [544] - 711 |
| Physical Description: | XIII, 746 S. |
| ISBN: | 3540512500 0387512500 |
Staff View
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| 245 | 1 | 0 | |a Elementary and analytic theory of algebraic numbers |c Władysław Narkiewicz |
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Record in the Search Index
| _version_ | 1804117014744137728 |
|---|---|
| adam_text | Wladyslaw Narkiewicz
Elementary
and Analytic Theory
of Algebraic Numbers
Second Edition, Substantially Revised and Extended
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo Hong Kong
PWN—Polish Scientific Publishers
Warszawa
Table of Contents
Preface VII
Chapter 1 Dedekind Rings and Valuations 1
§ 1 Dedekind Rings 1
§ 2 Valuations and Exponents IS
§ 3 Finitely Generated Modules over Dedekind Domains 23
§ 4 Notes to Chapter 1 35
Exercises to Chapter 1 41
Chapter 2 Algebraic Numbers and Integers 42
§ 1 Distribution of Integers in the Complex Plane 42
§ 2 Discriminants and Integral Bases 52
§ 3 Applications of Minkowski s Convex Body Theorem 66
§ 4 Notes to Chapter 2 71
Exercises to Chapter 2 84
Chapter 3 Units and Ideal Classes 86
§ 1 Valuations of Algebraic Number Fields 86
§ 2 Ideal Classes : 94
§3 Units 99
§ 4 Euclidean Algorithm 120
§ 5 Notes to Chapter 3 125
Exercises to Chapter 3 142
Chapter 4 Extensions 143
§ 1 The Homomorphisms of Injection and Norm 143
§ 2 Different and Discriminant 155
§ 3 Factorization of Prime Ideals in Extensions More about
the Class-Group 175
§ 4 Notes to Chapter 4 193
Exercises to Chapter 4 206
XII Table of Contents
Chapter 5 p-adic Fields 207
§ 1 Principal Properties, Integers, Units 207
§2 Extensions of p-adic Fields 229
§ 3 Harmonic Analysis in p-adic Fields 244
§ 4 Notes to Chapter 5 259
Exercises to Chapter 5 264
Chapter 6 Applications of the Theory of p-adic Fields to Algebraic
Number Fields 265
§ 1 Arithmetic Applications 265
§ 2 Adeles and Ideles 295
§ 3 Notes to Chapter 6 317
Exercises to Chapter 6 322
Chapter 7 Analytical Methods 324
§ 1 The Classical Zeta-Functions 324
§ 2 Asymptotic Distribution of Ideals and Prime Ideals 355
§ 3 Chebotarev s Theorem 379
§ 4 Notes to Chapter 7 404
Exercises to Chapter 7 418
Chapter 8 Abelian Fields 421
§ 1 Main Properties 421
§ 2 The Class-Number Formula and the Siegel-Brauer Theorem 436
§ 3 Class-Number of Quadratic Fields 448
§ 4 Notes to Chapter 8 470
Exercises to Chapter 8 488
Chapter 9 Factorization Problems 490
§ 1 Elementary Approach to Factorizations 490
§ 2 Quantitative Results 501
§ 3 Notes to Chapter 9 511
Exercises to Chapter 9 519
Appendix I Locally Compact Abelian Groups 520
Appendix II Dirichlet Series 534
Appendix III Geometry of Numbers 536
Appendix IV Baker s Method 538
Table of Contents XIII
Unsolved Problems 539
Bibliography 544
List of Important Symbols , 713
Subject Index 715
Author Index 723
Addendum 743
|
| any_adam_object | 1 |
| author | Narkiewicz, Władysław 1936- |
| author_GND | (DE-588)11036676X |
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| author_sort | Narkiewicz, Władysław 1936- |
| author_variant | w n wn |
| building | Verbundindex |
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| ctrlnum | (OCoLC)20262723 (DE-599)BVBBV002633024 |
| dewey-full | 512/.74 |
| 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 |
| edition | 2. ed., substantially rev. and extended |
| format | Book |
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| indexdate | 2024-07-09T15:47:40Z |
| institution | BVB |
| isbn | 3540512500 0387512500 |
| language | English |
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| physical | XIII, 746 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
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| publisher | Springer u.a. |
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| spelling | Narkiewicz, Władysław 1936- Verfasser (DE-588)11036676X aut Elementary and analytic theory of algebraic numbers Władysław Narkiewicz 2. ed., substantially rev. and extended Berlin u.a. Springer u.a. 1990 XIII, 746 S. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. [544] - 711 Nombres algébriques, théorie des ram Algebraic number theory Algebraische Zahl (DE-588)4141847-5 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Analytische Zahlentheorie (DE-588)4001870-2 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 s DE-604 Algebraische Zahl (DE-588)4141847-5 s DE-188 Analytische Zahlentheorie (DE-588)4001870-2 s 1\p DE-604 Zahlentheorie (DE-588)4067277-3 s 2\p DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001690318&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Narkiewicz, Władysław 1936- Elementary and analytic theory of algebraic numbers Nombres algébriques, théorie des ram Algebraic number theory Algebraische Zahl (DE-588)4141847-5 gnd Zahlentheorie (DE-588)4067277-3 gnd Analytische Zahlentheorie (DE-588)4001870-2 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| subject_GND | (DE-588)4141847-5 (DE-588)4067277-3 (DE-588)4001870-2 (DE-588)4001170-7 |
| title | Elementary and analytic theory of algebraic numbers |
| title_auth | Elementary and analytic theory of algebraic numbers |
| title_exact_search | Elementary and analytic theory of algebraic numbers |
| title_full | Elementary and analytic theory of algebraic numbers Władysław Narkiewicz |
| title_fullStr | Elementary and analytic theory of algebraic numbers Władysław Narkiewicz |
| title_full_unstemmed | Elementary and analytic theory of algebraic numbers Władysław Narkiewicz |
| title_short | Elementary and analytic theory of algebraic numbers |
| title_sort | elementary and analytic theory of algebraic numbers |
| topic | Nombres algébriques, théorie des ram Algebraic number theory Algebraische Zahl (DE-588)4141847-5 gnd Zahlentheorie (DE-588)4067277-3 gnd Analytische Zahlentheorie (DE-588)4001870-2 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| topic_facet | Nombres algébriques, théorie des Algebraic number theory Algebraische Zahl Zahlentheorie Analytische Zahlentheorie Algebraische Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001690318&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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