Sets of multiples:
The theory of sets of multiples, a subject which lies at the intersection of analytic and probabilistic number theory, has seen much development since the publication of 'Sequences' by Halberstam and Roth nearly thirty years ago. The area is rich in problems, many of them still unsolved or...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1996
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
118 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | The theory of sets of multiples, a subject which lies at the intersection of analytic and probabilistic number theory, has seen much development since the publication of 'Sequences' by Halberstam and Roth nearly thirty years ago. The area is rich in problems, many of them still unsolved or arising from current work. The author sets out to give a coherent, essentially self-contained account of the existing theory and at the same time to bring the reader to the frontiers of research. One of the fascinations of the theory is the variety of methods applicable to it, which include Fourier analysis, group theory, high and ultra-low moments, probability and elementary inequalities, as well as several branches of number theory. This Tract is the first devoted to the subject, and will be of value to number theorists, whether they be research workers or graduate students. |
| Physical Description: | XVI, 264 S. |
| ISBN: | 052140424X |
Staff View
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| 520 | 3 | |a The theory of sets of multiples, a subject which lies at the intersection of analytic and probabilistic number theory, has seen much development since the publication of 'Sequences' by Halberstam and Roth nearly thirty years ago. The area is rich in problems, many of them still unsolved or arising from current work. The author sets out to give a coherent, essentially self-contained account of the existing theory and at the same time to bring the reader to the frontiers of research. One of the fascinations of the theory is the variety of methods applicable to it, which include Fourier analysis, group theory, high and ultra-low moments, probability and elementary inequalities, as well as several branches of number theory. This Tract is the first devoted to the subject, and will be of value to number theorists, whether they be research workers or graduate students. | |
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| adam_text | Contents
Preface page ix
Introduction xi
Notation xv
0 First ideas 1
0.1 Introduction 1
0.2 Sets of multiples and primitive sequences 1
0.3 Densities 3
0.4 The Heilbronn Rohrbach and Behrend inequalities 13
0.5 Total decomposition sets 22
1 Besicovitch and Behrend sequences 26
1.1 Introduction 26
1.2 Erdos criterion 26
1.3 Behrend sequences 36
1.4 Witnesses 60
2 Derived sequences and densities 66
2.1 Introduction 66
2.2 Upper bounds for tk(sf) 68
2.3 Generalized Behrend inequalities 82
2.4 Multilinear functions 88
2.5 Formulae for the densities tk(jtf) 91
3 Oscillation 96
3.1 Introduction 96
3.2 A first lower bound for (s/, st) 105
3.3 Upper bounds for (s/,rf) 112
3.4 Primitive.*/ 117
3.5 Perfect sequences 122
vii
viii Contents
4 Probabilistic group theory 126
4.1 Introduction 126
4.2 The Erdos Renyi theorem: first variant 130
4.3 The Erdos Renyi theorem: second variant 146
4.4 The Behrend sequences s/ (t) 153
4.5 A conjecture of Erdos and Renyi 167
5 Divisor density 170
5.1 Introduction 170
5.2 Necessary and sufficient conditions 179
5.3 Slowly switching sequences 192
5.4 Slowly switching sequences: a reformulation 198
6 Divisor uniform distribution 203
6.1 Introduction 203
6.2 Applications of divisor density 205
6.3 Weyl sums and additive functions 213
6.4 Weyl sums and discrepancy 218
6.5 Lower bounds for discrepancy 226
7 H(x,y,z) 239
7.1 Introduction 239
7.2 Short intervals 240
7.3 The asymptotic formula for YL ^ 244
7.4 The asymptotic formula for H(x,y,z) 250
Bibliography 258
Index 263
|
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| indexdate | 2024-07-09T18:04:21Z |
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| isbn | 052140424X |
| language | English |
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| physical | XVI, 264 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | Cambridge Univ. Press |
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| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Hall, Richard R. Verfasser aut Sets of multiples Richard R. Hall 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1996 XVI, 264 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 118 The theory of sets of multiples, a subject which lies at the intersection of analytic and probabilistic number theory, has seen much development since the publication of 'Sequences' by Halberstam and Roth nearly thirty years ago. The area is rich in problems, many of them still unsolved or arising from current work. The author sets out to give a coherent, essentially self-contained account of the existing theory and at the same time to bring the reader to the frontiers of research. One of the fascinations of the theory is the variety of methods applicable to it, which include Fourier analysis, group theory, high and ultra-low moments, probability and elementary inequalities, as well as several branches of number theory. This Tract is the first devoted to the subject, and will be of value to number theorists, whether they be research workers or graduate students. Reeksen (wiskunde) gtt Suites (Mathématiques) ram Sequences (Mathematics) Sequentialanalyse (DE-588)4128461-6 gnd rswk-swf Sequentialanalyse (DE-588)4128461-6 s DE-604 Cambridge tracts in mathematics 118 (DE-604)BV000000001 118 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007452512&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hall, Richard R. Sets of multiples Cambridge tracts in mathematics Reeksen (wiskunde) gtt Suites (Mathématiques) ram Sequences (Mathematics) Sequentialanalyse (DE-588)4128461-6 gnd |
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| title | Sets of multiples |
| title_auth | Sets of multiples |
| title_exact_search | Sets of multiples |
| title_full | Sets of multiples Richard R. Hall |
| title_fullStr | Sets of multiples Richard R. Hall |
| title_full_unstemmed | Sets of multiples Richard R. Hall |
| title_short | Sets of multiples |
| title_sort | sets of multiples |
| topic | Reeksen (wiskunde) gtt Suites (Mathématiques) ram Sequences (Mathematics) Sequentialanalyse (DE-588)4128461-6 gnd |
| topic_facet | Reeksen (wiskunde) Suites (Mathématiques) Sequences (Mathematics) Sequentialanalyse |
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