Metric number theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon
1998
|
| Schriftenreihe: | London Mathematical Society: [London Mathematical Society monographs / New series]
18 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 297 S. |
| ISBN: | 0198500831 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Contents
Notation xiii
Introduction xv
1 Normal numbers 1
1.1 Definitions and elementary properties 1
1.2 Metrical lemmas and Borel s theorem 7
1.3 The law of the iterated logarithm 18
Notes 23
2 Diophantine approximation 24
2.1 Statement of results 24
2.2 Zero one laws 29
2.3 The Duffin and Schaeffer theorem 37
2.4 Vaaler s theorem 44
2.5 Proof of Theorems 2.3 and 2.8 51
2.6 The Duffin and Schaeffer conjecture reformulated 53
Notes 58
3 GCD sums with applications 60
3.1 Statement of results 60
3.2 Proof of Theorem 3.1 67
3.3 Proof of Theorem 3.2 70
3.4 Proof of Theorems 3.3 and 3.4 78
3.5 Proof of Theorem 3.5 82
3.6 Proof of Theorems 3.6 and 3.7 86
3.7 Proof of Theorem 3.8 91
Notes 93
4 Schmidt s method 94
4.1 Statement of results 94
4.2 Proof of Theorems 4.1 and 4.2 97
4.3 Proof of Theorem 4.3 105
4.4 Proof of Theorem 4.4 109
4.5 The metric theory of continued fractions 112
4.6 A generalization to higher dimensions 115
Notes 118
x Contents
5 Uniform distribution 120
5.1 Definitions and elementary properties 120
5.2 Trigonometric sums, the Erdos Turan theorem and
the Weyl criterion 126
5.3 The metrical theory of uniform distribution 131
5.4 Uniform distribution in higher dimensions 151
Notes 161
6 Diophantine approximation with
restricted numerator and denominator 164
6.1 Introduction and statement of results 164
6.2 Proof of Theorem 6.2 171
6.3 Proof of Theorem 6.3 175
6.4 Proof of Theorem 6.4 177
6.5 Proof of Theorems 6.5 and 6.6 179
6.6 Proof of Theorem 6.7 180
Notes 186
7 Non integer sequences 187
7.1 Introduction and statement of results 187
7.2 Proof of Theorems 7.1 and 7.2 192
7.3 A reduction of the problem and
proofs for Theorems 7.3 and 7.5 198
7.4 Proof of Theorem 7.4 202
7.5 Proof of Theorem 7.6 206
7.6 Proof of Theorems 7.7 and 7.8 211
Notes 213
8 The integer parts of sequences 215
8.1 Introduction and statement of results 215
8.2 Proof of Theorem 8.1 220
8.3 Proof of Theorem 8.2 226
8.4 Proof of Theorem 8.3 229
8.5 Proof of Theorem 8.4 233
8.6 Proof of Theorem 8.5 234
8.7 Proof of Theorem 8.6 237
8.8 Proof of Theorem 8.7 238
Notes 240
9 Diophantine approximation on manifolds 241
9.1 Introduction 241
9.2 Proof of Theorem 9.2 245
9.3 Proof of Theorem 9.3 256
Notes 261
Contents xi
10 Hausdorff dimension of exceptional sets 262
10.1 Introduction and statement of results 262
10.2 Proof of Theorems 10.1 and 10.2 266
10.3 Proof of Theorems 10.3 and 10.4 267
10.4 Proof of Theorems 10.5, 10.6, and 10.7 271
10.5 Proof of Theorem 10.8 276
Notes 278
References 280
Index 295
|
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| id | DE-604.BV011991532 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:19:48Z |
| institution | BVB |
| isbn | 0198500831 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008114867 |
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| physical | XVIII, 297 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
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| publisher | Clarendon |
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| series2 | London Mathematical Society: [London Mathematical Society monographs / New series] |
| spelling | Harman, Glyn Verfasser aut Metric number theory Glyn Harman Oxford Clarendon 1998 XVIII, 297 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: [London Mathematical Society monographs / New series] 18 Number theory Reelle Zahl (DE-588)4202628-3 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 Reelle Zahl (DE-588)4202628-3 s Maßtheorie (DE-588)4074626-4 s New series] London Mathematical Society: [London Mathematical Society monographs 18 (DE-604)BV045355493 18 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008114867&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Harman, Glyn Metric number theory Number theory Reelle Zahl (DE-588)4202628-3 gnd Maßtheorie (DE-588)4074626-4 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4202628-3 (DE-588)4074626-4 (DE-588)4067277-3 |
| title | Metric number theory |
| title_auth | Metric number theory |
| title_exact_search | Metric number theory |
| title_full | Metric number theory Glyn Harman |
| title_fullStr | Metric number theory Glyn Harman |
| title_full_unstemmed | Metric number theory Glyn Harman |
| title_short | Metric number theory |
| title_sort | metric number theory |
| topic | Number theory Reelle Zahl (DE-588)4202628-3 gnd Maßtheorie (DE-588)4074626-4 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Number theory Reelle Zahl Maßtheorie Zahlentheorie |
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