Additive theory of prime numbers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Providence, RI
Providence, RI
1966
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| Ausgabe: | 2. print. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
Internformat
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Datensatz im Suchindex
| _version_ | 1804128281370296320 |
|---|---|
| adam_text | TABLE OF CONTENTS
Foreword vii
Preface to the present edition ix
Preface to the 1953 Chinese edition ix
Preface to the Russian edition x
Preface originally intended for the Russian edition xi
Explanatory remarks xiii
Chapter I. Trigonometric sums 1
§1. Statement of a theorem and a Fundamental Lemma 1
§2. Proof of the theorem from the Fundamental Lemma 1
§3. Proof of the Fundamental Lemma for the case 1=1 (Mordell) 3
§4. Some lemmas 4
§5. Proof of the Fundamental Lemma 5
§6. Corollaries 7
§7. Finite Fourier series 9
§8. Formulation and proof of Theorem 2 10
Chapter II. Estimates for sums involving the divisor function d(n) 11
§1. Formulation of Theorem 3 11
§2. Van der Corput s lemma 11
§3. Lemmas pertaining to the number of solutions of congruences 14
§4. Proof of the theorem 16
§5. Further lemmas 17
Chapter III. Mean value theorems for certain trigonometric sums (I) 19
§1. Formulation of Theorem 4 19
§2. Certain lemmas pertaining to inequalities 19
§3. Proof of the theorem 22
§4. Weyl s lemma 23
Chapter IV. Vinogradov s mean value theorem and its corollaries 26
§1. Description of the theorem 26
§2. Lemmas 27
§3. Proof of the theorem 30
iii
iv TABLE OF CONTENTS
§4. Corollary 36
¦§5 Lemmas on convex functions 37
Chapter V. Mean value theorems for certain trigonometric sums (II) 40
§1. Formulation of Theorems 7 and 8 40
§2. Remarks concerning theorems A^ (i.e., Theorem 8) 41
§3. An estimate of two integrals by means of symmetric functions 42
§4. A further lemma 46
§5 Proof of the theorems 47
§6. Proof of the theorems (continued) 52
§7. The relation between a single sum and the mean value 56
§8. Estimates for trigonometric sums 62
Chapter VI. Trigonometric sums depending on prime numbers 66
§1. Formulation of Theorem 10 66
§2. Certain essential lemmas 66
§3. Proof of the theorem 73
Chapter VII. An asymptotic formula for the number of solutions of
the Waring Goldbach problem 78
§1. Formulation of Theorem 11 78
§2. Certain lemmas 79
§3. Farey s dissection 85
§4. An estimate of the absolute value of an integral taken over E 86
§5 Lemmas concerning 3H(h, g) 87
§6. An estimate of the absolute value of an integral taken over 3R(A, g) 89
§7. Lemmas essential for the proof of the theorem 90
§8. Proof of the theorem 94
§9. Proof of the theorem (conclusion) 96
Chapter VIE. Singular series 100
§1. Formulation of Theorem 12 100
§2. Lemmas pertaining to trigonometric sums 100
§3. Lemmas pertaining to congruences 103
§4. Positiveness of the singular series 106
§5. Corollaries of Theorems 11 and 12 108
Chapter IX. A further study of the Waring Goldbach problem 109
§1. Introduction 109
§2. Davenport s lemma 112
TABLE OF CONTENTS v
§3. Proof of Theorem 13 114
§4. Appendix 117
Chapter X. Indeterminate equations in prime unknowns 124
§1. Introduction 124
§2. Lemmas necessary for the proof of Theorem 16 124
§3 Results related to Tarry s problem 130
§4. Formulation of Theorem 16 139
§5. Proof of the theorem 140
§6. Appendix 149
Chapter XI. A further study of the problem of the preceding chapter 157
§1. Introduction 157
§2. A study of the condition of positive solvability 157
§3. Singular series and the condition of congruent solvability 162
§4. Some lemmas 170
§5. A lemma 171
§6. A further lemma 173
Chapter XII. Other results 175
§1. Introduction 175
§2. Definitions 175
§3 Formulation of a conjecture 176
§4. Application of the method of Chapters X and XI to a general
problem 178
§5 Statement of a further conjecture 178
§6. Further results 179
Appendix 181
|
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| author | Hua, Luogeng 1910-1985 |
| author_GND | (DE-588)119001500 |
| author_facet | Hua, Luogeng 1910-1985 |
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| author_sort | Hua, Luogeng 1910-1985 |
| author_variant | l h lh |
| building | Verbundindex |
| bvnumber | BV013491267 |
| classification_rvk | SK 180 |
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| discipline | Mathematik |
| edition | 2. print. |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:46:45Z |
| institution | BVB |
| language | Undetermined |
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| publisher | Providence, RI |
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| spelling | Hua, Luogeng 1910-1985 Verfasser (DE-588)119001500 aut Additive theory of prime numbers 2. print. Providence, RI Providence, RI 1966 txt rdacontent n rdamedia nc rdacarrier Primzahltheorie (DE-588)4175715-4 gnd rswk-swf Primzahl (DE-588)4047263-2 gnd rswk-swf Additive Primzahltheorie (DE-588)4141385-4 gnd rswk-swf Primzahl (DE-588)4047263-2 s DE-604 Additive Primzahltheorie (DE-588)4141385-4 s 1\p DE-604 Primzahltheorie (DE-588)4175715-4 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009207834&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 | Hua, Luogeng 1910-1985 Additive theory of prime numbers Primzahltheorie (DE-588)4175715-4 gnd Primzahl (DE-588)4047263-2 gnd Additive Primzahltheorie (DE-588)4141385-4 gnd |
| subject_GND | (DE-588)4175715-4 (DE-588)4047263-2 (DE-588)4141385-4 |
| title | Additive theory of prime numbers |
| title_auth | Additive theory of prime numbers |
| title_exact_search | Additive theory of prime numbers |
| title_full | Additive theory of prime numbers |
| title_fullStr | Additive theory of prime numbers |
| title_full_unstemmed | Additive theory of prime numbers |
| title_short | Additive theory of prime numbers |
| title_sort | additive theory of prime numbers |
| topic | Primzahltheorie (DE-588)4175715-4 gnd Primzahl (DE-588)4047263-2 gnd Additive Primzahltheorie (DE-588)4141385-4 gnd |
| topic_facet | Primzahltheorie Primzahl Additive Primzahltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009207834&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hualuogeng additivetheoryofprimenumbers |