Diophantine equations and inequalities in algebraic number fields:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1991
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 163 - 167 |
| Physical Description: | XVI, 168 S. |
| ISBN: | 3540520198 0387520198 |
Staff View
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Record in the Search Index
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| adam_text |
Contents
Introduction IX
Notation XV
Chapter 1. The Circle Method and Waring's Problem
1.1 Introduction 1
1.2 Faxey Division 1
1.3 Auxiliary Lemmas 3
1.4 Major Arcs 3
1.5 Singular Integral 6
1.6 Singular Series 8
1.7 Proof of Lemma 1.12 10
1.8 Proof of Theorem 1.1 12
Notes 13
Chapter 2. Complete Exponential Sums
2.1 Introduction 14
2.2 Several Lemmas 15
2.3 Mordell's Lemma 17
2.4 Fundamental Lemma 19
2.5 Proof of Theorem 2.1 21
2.6 Proof of Theorem 2.2 21
Notes 22
Chapter 3. Weyl's Sums
3.1 Introduction 23
3.2 Proof of Theorem 3.1 24
3.3 A Lemma on Units 25
3.4 The Asymptotic Formula for N(a,T) 27
3.5 A Sum 30
3.6 Mitsui's Lemma 31
3.7 Proof of Theorem 3.3 34
3.8 Proof of Lemma 3.6 35
3.9 Continuation 39
Notes 43
Chapter 4. Mean Value Theorems
4.1 Introduction 44
4.2 Proof of Theorem 4.1 44
4.3 Proof of Theorem 4.2 46
4.4 A Lemma on the Set D 47
4.5 A Lemma on the Set D(x) 49
4.6 Fundamental Lemma 52
VI
4.7 Proof of Lemma 4.1 56
Notes 57
Chapter 5. The Circle Method in Algebraic Number Fields
5.1 Introduction 58
5.2 Lemmas 61
5.3 Asympotic Expansion for Si(£,T) 64
5.4 Further Estimates on Basic Domains 66
5.5 Proof of Theorem 5.1 69
5.6 Proof of Theorem 5.2 70
Notes 71
Chapter 6. Singular Series and Singular Integrals
6.1 Introduction 72
6.2 Product Form for Singular Series 73
6.3 Singular Series and Congruences 75
6.4 p adic Valuations 76
6.5 fc th Power Residues 78
6.6 Proof of Theorem 6.1 79
6.7 Monotonic Functions 80
6.8 Proof of Theorem 6.2 83
Notes 86
Chapter 7. Waring's Problem
7.1 Introduction 87
7.2 The Ring Jk 89
7.3 Proofs of Theorems 7.1 and 7.2 92
7.4 Proof of Theorem 7.3 93
7.5 Proof of Theorem 7.4 95
Notes 96
Chapter 8. Additive Equations
8.1 Introduction 98
8.2 Reductions 99
8.3 Contraction 100
8.4 Derived Variables 102
8.5 Proof of Theorem 8.1 103
8.6 Proof of Theorem 8.2 105
8.7 Bounds for Solutions 108
Notes 110
Chapter 9. Small Nonnegative Solutions of Additive Equations
9.1 Introduction Ill
9.2 Hurwitz's Lemma Ill
VII
9.3 Reductions 113
9.4 Continuation 116
9.5 Farey Division 118
9.6 Supplementary Domain 119
9.7 Basic Domains 121
9.8 Proof of Theorem 9.1 125
Notes 126
Chapter 10. Small Solutions of Additive Equations
10.1 Introduction 127
10.2 Reductions 127
10.3 Continuation 129
10.4 Farey Division 132
10.5 Supplementary Domain 133
10.6 Basic Domains 137
10.7 Proof of Theorem 10.1 139
Notes 139
Chapter 11. Diophantine Inequalities for Forms
11.1 Introduction 140
11.2 A Single Additive Form 142
11.3 A Variant Circle Method 144
11.4 Continuation 147
11.5 Proof of Lemma 11.1 150
11.6 Linear Forms 153
11.7 A Single Form 154
11.8 Proof of Theorem 11.1 158
Notes 159
References I 163
References II 164
Index 168 |
| any_adam_object | 1 |
| author | Wang, Yuan 1930- |
| author_GND | (DE-588)120999072 |
| author_facet | Wang, Yuan 1930- |
| author_role | aut |
| author_sort | Wang, Yuan 1930- |
| author_variant | y w yw |
| building | Verbundindex |
| bvnumber | BV004514923 |
| classification_rvk | SK 180 |
| classification_tum | MAT 102f |
| ctrlnum | (OCoLC)260157337 (DE-599)BVBBV004514923 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004514923 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-30T00:09:33Z |
| institution | BVB |
| isbn | 3540520198 0387520198 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002781580 |
| oclc_num | 260157337 |
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| physical | XVI, 168 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| spelling | Wang, Yuan 1930- Verfasser (DE-588)120999072 aut Diophantine equations and inequalities in algebraic number fields Wang Yuan Berlin u.a. Springer 1991 XVI, 168 S. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 163 - 167 Diophantische Gleichung (DE-588)4012386-8 gnd rswk-swf Waringsches Problem (DE-588)4260442-4 gnd rswk-swf Kreismethode (DE-588)4260441-2 gnd rswk-swf Diophantische Ungleichung (DE-588)4200628-4 gnd rswk-swf Algebraischer Zahlkörper (DE-588)4068537-8 gnd rswk-swf Diophantische Gleichung (DE-588)4012386-8 s Algebraischer Zahlkörper (DE-588)4068537-8 s DE-604 Diophantische Ungleichung (DE-588)4200628-4 s DE-188 Waringsches Problem (DE-588)4260442-4 s Kreismethode (DE-588)4260441-2 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002781580&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wang, Yuan 1930- Diophantine equations and inequalities in algebraic number fields Diophantische Gleichung (DE-588)4012386-8 gnd Waringsches Problem (DE-588)4260442-4 gnd Kreismethode (DE-588)4260441-2 gnd Diophantische Ungleichung (DE-588)4200628-4 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd |
| subject_GND | (DE-588)4012386-8 (DE-588)4260442-4 (DE-588)4260441-2 (DE-588)4200628-4 (DE-588)4068537-8 |
| title | Diophantine equations and inequalities in algebraic number fields |
| title_auth | Diophantine equations and inequalities in algebraic number fields |
| title_exact_search | Diophantine equations and inequalities in algebraic number fields |
| title_full | Diophantine equations and inequalities in algebraic number fields Wang Yuan |
| title_fullStr | Diophantine equations and inequalities in algebraic number fields Wang Yuan |
| title_full_unstemmed | Diophantine equations and inequalities in algebraic number fields Wang Yuan |
| title_short | Diophantine equations and inequalities in algebraic number fields |
| title_sort | diophantine equations and inequalities in algebraic number fields |
| topic | Diophantische Gleichung (DE-588)4012386-8 gnd Waringsches Problem (DE-588)4260442-4 gnd Kreismethode (DE-588)4260441-2 gnd Diophantische Ungleichung (DE-588)4200628-4 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd |
| topic_facet | Diophantische Gleichung Waringsches Problem Kreismethode Diophantische Ungleichung Algebraischer Zahlkörper |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002781580&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wangyuan diophantineequationsandinequalitiesinalgebraicnumberfields |