Divisors:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Univ. Press
1988
|
| Schriftenreihe: | Cambridge tracts in mathematics
90 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 167 S. |
| ISBN: | 052134056X |
Internformat
MARC
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| 100 | 1 | |a Hall, Richard R. |e Verfasser |0 (DE-588)142400912 |4 aut | |
| 245 | 1 | 0 | |a Divisors |c Richard R. Hall ; Gérald Tenenbaum |
| 264 | 1 | |a Cambridge [u.a.] |b Univ. Press |c 1988 | |
| 300 | |a XVI, 167 S. | ||
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| 490 | 1 | |a Cambridge tracts in mathematics |v 90 | |
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Datensatz im Suchindex
| _version_ | 1817484626080301056 |
|---|---|
| adam_text |
Contents
Preface xi
Notation xv
0 Preliminaries 1
0.1 Introduction 1
0.2 Sums of multiplicative functions 1
0.3 Sieve estimates 4
0.4 Local distributions of prime factors and Poisson variables 4
0.5 A general principle 6
Notes on Chapter 0 9
Exercises on Chapter 0 11
1 The normal distribution of the prime factors 14
1.1 The law of the iterated logarithm 14
1.2 The normal size of p,(n) and dj(n) 21
Notes on Chapter 1 24
Exercises on Chapter 1 25
2 Sieving by an interval 27
2.1 Introduction 27
2.2 Statement of results concerning H(x, y, z) 29
2.3 More applications 31
2.4 Proof of Theorem 22 34
2.5 Proof of Theorem 21 (i) small z 38
2.6 Proof of Theorem 21 (ii), (iii) upper bounds 40
2.7 Proof of Theorem 21 (ii), (iii) lower bounds 41
2.8 Proof of Theorem 21 (iv) large z 46
Notes on Chapter 2 48
Exercises on Chapter 2 49
3 Imaginary powers 52
3.1 Introduction 52
viii Contents
3.2 A p.p. upper bound for |t(h, 6)\ 52
3.3 Ratios of divisors 56
3.4 Average orders 57
Notes on Chapter 3 62
Exercises on Chapter 3 64
4 Measures of propinquity 65
4.1 Introduction 65
4.2 T and U preliminary matters 65
4.3 T and U average orders 67
4.4 The normal orders of log T and log U 74
4.5 The function T(n,0)/T(n) 79
4.6Erdos' function r + (n) 83
4.7 Hooley's function A(«) 89
Notes on Chapter 4 92
Exercises on Chapter 4 93
5 Erdos' conjecture 95
5.1 Introduction and results 95
5.2 Proof of Theorem 50 99
5.3 Proof of Theorem 51 104
5.4 A p.p. upper bound for the A function HI
Notes on Chapter 5 118
Exercises on Chapter 5 120
6 Hooley's Ar functions sharp bounds 121
6.1 Introduction 121
6.2 Lower bounds 122
6.3 The critical interval 123
6.4 Technical preparation 124
6.5 Iteration inequalities 126
6.6 Small y the lower bound for A~ 127
6.7 Fourier transforms initial treatment 128
6.8 Fourier transforms an upper bound for Ar+ 132
Notes on Chapter 6 136
Exercises on Chapter 6 138
7 Hooley's Ar functions the critical interval 139
7.1 Introduction 139
7.2 Notation. The fundamental lemma 140
7.3 First variant differential inequalities 146
Contents ix
7.4 Second variant double induction 150
Notes on Chapter 7 156
Exercises on Chapter 7 157
Appendix: Distribution functions 158
Bibliography 161
Index 165 |
| any_adam_object | 1 |
| author | Hall, Richard R. Tenenbaum, Gérald 1952- |
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| author_facet | Hall, Richard R. Tenenbaum, Gérald 1952- |
| author_role | aut aut |
| author_sort | Hall, Richard R. |
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| building | Verbundindex |
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| callnumber-first | Q - Science |
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| callnumber-raw | QA242 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 SK 800 |
| classification_tum | MAT 105f |
| ctrlnum | (OCoLC)16581787 (DE-599)BVBBV001288836 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-12-04T05:00:08Z |
| institution | BVB |
| isbn | 052134056X |
| language | English |
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| physical | XVI, 167 S. |
| publishDate | 1988 |
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| publisher | Univ. Press |
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| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Hall, Richard R. Verfasser (DE-588)142400912 aut Divisors Richard R. Hall ; Gérald Tenenbaum Cambridge [u.a.] Univ. Press 1988 XVI, 167 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 90 Distribution (Théorie des probabilités) ram Diviseurs, Théorie des ram Getaltheorie gtt Verdelingen (statistiek) gtt Distribution (Probability theory) Divisor theory Divisor (DE-588)4150324-7 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Divisor (DE-588)4150324-7 s DE-604 Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s Tenenbaum, Gérald 1952- Verfasser (DE-588)1066273146 aut Cambridge tracts in mathematics 90 (DE-604)BV000000001 90 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000777251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hall, Richard R. Tenenbaum, Gérald 1952- Divisors Cambridge tracts in mathematics Distribution (Théorie des probabilités) ram Diviseurs, Théorie des ram Getaltheorie gtt Verdelingen (statistiek) gtt Distribution (Probability theory) Divisor theory Divisor (DE-588)4150324-7 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| subject_GND | (DE-588)4150324-7 (DE-588)4121894-2 |
| title | Divisors |
| title_auth | Divisors |
| title_exact_search | Divisors |
| title_full | Divisors Richard R. Hall ; Gérald Tenenbaum |
| title_fullStr | Divisors Richard R. Hall ; Gérald Tenenbaum |
| title_full_unstemmed | Divisors Richard R. Hall ; Gérald Tenenbaum |
| title_short | Divisors |
| title_sort | divisors |
| topic | Distribution (Théorie des probabilités) ram Diviseurs, Théorie des ram Getaltheorie gtt Verdelingen (statistiek) gtt Distribution (Probability theory) Divisor theory Divisor (DE-588)4150324-7 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| topic_facet | Distribution (Théorie des probabilités) Diviseurs, Théorie des Getaltheorie Verdelingen (statistiek) Distribution (Probability theory) Divisor theory Divisor Wahrscheinlichkeitsverteilung |
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