An introduction to the geometry of numbers:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1997
|
| Edition: | Reprint of the 1971 ed. |
| Series: | Classics in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Auch als: Grundlehren der mathematischen Wissenschaften ; Vol. 99 Literaturverz. S. 334 - 343 |
| Physical Description: | VII, 344 S. graph. Darst. |
| ISBN: | 3540617884 |
Staff View
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Record in the Search Index
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| adam_text | J.W.S.CASSELS AN INTRODUCTION TO THE GEOMETRY OF NUMBERS SECOND
PRINTING, CORRECTED SPRINGER-VERLAG BERLIN * HEIDELBERG * NEW YORK 1971
CONTENTS PAGE NOTATION VIII PROLOGUE 1 CHAPTER I. LATTICES 9 1.
INTRODUCTION 9 2. BASES AND SUBLATTICES 9 3. LATTICES UNDER LINEAR
TRANSFORMATION 19 4. FORMS AND LATTICES 20 5. THE POLAR LATTICE 23
CHAPTER II. REDUCTION 26 1. INTRODUCTION 26 2. THE BASIC PROCESS 27 3.
DEFINITE QUADRATIC FORMS 30 4. INDEFINITE QUADRATIC FORMS 35 5. BINARY
CUBIC FORMS 51 6. OTHER FORMS 60 CHAPTER III. THEOREMS OF BLICHFELDT AND
MINKOWSKI 64 1. INTRODUCTION 64 2. BLICHFELDT S AND MINKOWSKI S THEOREMS
* 68 3. GENERALISATIONS TO NON-NEGATIVE FUNCTIONS 73 4. CHARACTERISATION
OF LATTICES 78 5. LATTICE CONSTANTS 80 6. A METHOD OF MORDELL 84 7.
REPRESENTATION OF INTEGERS BY QUADRATIC FORMS 98 CHAPTER IV. DISTANCE
FUNCTIONS 103 1. INTRODUCTION 103 2. GENERAL DISTANCE-FUNCTIONS 105 3.
CONVEX SETS 108 4. DISTANCE FUNCTIONS AND LATTICES 119 CHAPTER V.
MAHLER S COMPACTNESS THEOREM 121 1. INTRODUCTION 121 2. LINEAR
TRANSFORMATIONS 122 3. CONVERGENCE OF LATTICES 126 4. COMPACTNESS FOR
LATTICES 134 5. CRITICAL LATTICES 141 6. BOUNDED STAR-BODIES 145 7.
REDUCIBILITY 152 8. CONVEX BODIES 155 9. SPHERES 163 10. APPLICATIONS TO
DIOPHANTINE APPROXIMATION 165 CHAPTER VI. THE THEOREM OF
MINKOWSKI-HLAWKA 175 1. INTRODUCTION 175 2. SUBLATTICES OF PRIME INDEX
17S CONTENTS VII PAGE 3. THE MINKOWSKI-HLAWKA THEOREM 181 4. SCHMIDT S
THEOREMS 184 5. A CONJECTURE OF ROGERS 187 6. UNBOUNDED STAR-BODIES 189
CHAPTER VII. THE QUOTIENT SPACE 194 1. INTRODUCTION 194 2. GENERAL
PROPERTIES 194 3. THE SUM THEOREM 198 CHAPTER VIII. SUCCESSIVE MINIMA
201 1. INTRODUCTION 201 2. SPHERES 205 3. GENERAL DISTANCE-FUNCTIONS 207
4. CONVEX SETS 213 5. POLAR CONVEX BODIES 219 CHAPTER IX. PACKINGS 223
1. INTRODUCTION 223 2. SETS WITH V(Y) = 1 N A{?) 228 3. VORONOI S
RESULTS 231 4. PREPARATORY LEMMAS 235 5. FETES T6TH S THEOREM 240 6.
CYLINDERS 245 7. PACKING OF SPHERES 246 8. THE PRODUCT OF N LINEAR FORMS
250 CHAPTER X. AUTOMORPHS 256 1. INTRODUCTION 256 2. SPECIAL FORMS 266
3. A METHOD OF MORDELL 268 4. EXISTENCE OF AUTOMORPHS 279 5. ISOLATION
THEOREMS 286 6. APPLICATIONS OF ISOLATION 295 7. AN INFINITY OF
SOLUTIONS 298 8. LOCAL METHODS 301 CHAPTER XI. INHOMOGENEOUS PROBLEMS
303 1. INTRODUCTION 303 2. CONVEX SETS 309 3. TRANSFERENCE THEOREMS FOR
CONVEX SETS 313 4. THE PRODUCT OF N LINEAR FORMS 322 APPENDIX 332
REFERENCES 334 INDEX 343
|
| adam_txt |
J.W.S.CASSELS AN INTRODUCTION TO THE GEOMETRY OF NUMBERS SECOND
PRINTING, CORRECTED SPRINGER-VERLAG BERLIN * HEIDELBERG * NEW YORK 1971
CONTENTS PAGE NOTATION VIII PROLOGUE 1 CHAPTER I. LATTICES 9 1.
INTRODUCTION 9 2. BASES AND SUBLATTICES 9 3. LATTICES UNDER LINEAR
TRANSFORMATION 19 4. FORMS AND LATTICES 20 5. THE POLAR LATTICE 23
CHAPTER II. REDUCTION 26 1. INTRODUCTION 26 2. THE BASIC PROCESS 27 3.
DEFINITE QUADRATIC FORMS 30 4. INDEFINITE QUADRATIC FORMS 35 5. BINARY
CUBIC FORMS 51 6. OTHER FORMS 60 CHAPTER III. THEOREMS OF BLICHFELDT AND
MINKOWSKI 64 1. INTRODUCTION 64 2. BLICHFELDT'S AND MINKOWSKI'S THEOREMS
* 68 3. GENERALISATIONS TO NON-NEGATIVE FUNCTIONS 73 4. CHARACTERISATION
OF LATTICES 78 5. LATTICE CONSTANTS 80 6. A METHOD OF MORDELL 84 7.
REPRESENTATION OF INTEGERS BY QUADRATIC FORMS 98 CHAPTER IV. DISTANCE
FUNCTIONS 103 1. INTRODUCTION 103 2. GENERAL DISTANCE-FUNCTIONS 105 3.
CONVEX SETS 108 4. DISTANCE FUNCTIONS AND LATTICES 119 CHAPTER V.
MAHLER'S COMPACTNESS THEOREM 121 1. INTRODUCTION 121 2. LINEAR
TRANSFORMATIONS 122 3. CONVERGENCE OF LATTICES 126 4. COMPACTNESS FOR
LATTICES 134 5. CRITICAL LATTICES 141 6. BOUNDED STAR-BODIES 145 7.
REDUCIBILITY 152 8. CONVEX BODIES 155 9. SPHERES 163 10. APPLICATIONS TO
DIOPHANTINE APPROXIMATION 165 CHAPTER VI. THE THEOREM OF
MINKOWSKI-HLAWKA 175 1. INTRODUCTION 175 2. SUBLATTICES OF PRIME INDEX
17S CONTENTS VII PAGE 3. THE MINKOWSKI-HLAWKA THEOREM 181 4. SCHMIDT'S
THEOREMS 184 5. A CONJECTURE OF ROGERS 187 6. UNBOUNDED STAR-BODIES 189
CHAPTER VII. THE QUOTIENT SPACE 194 1. INTRODUCTION 194 2. GENERAL
PROPERTIES 194 3. THE SUM THEOREM 198 CHAPTER VIII. SUCCESSIVE MINIMA
201 1. INTRODUCTION 201 2. SPHERES 205 3. GENERAL DISTANCE-FUNCTIONS 207
4. CONVEX SETS 213 5. POLAR CONVEX BODIES 219 CHAPTER IX. PACKINGS 223
1. INTRODUCTION 223 2. SETS WITH V(Y) = 1 N A{?) 228 3. VORONOI'S
RESULTS 231 4. PREPARATORY LEMMAS 235 5. FETES T6TH'S THEOREM 240 6.
CYLINDERS 245 7. PACKING OF SPHERES 246 8. THE PRODUCT OF N LINEAR FORMS
250 CHAPTER X. AUTOMORPHS 256 1. INTRODUCTION 256 2. SPECIAL FORMS 266
3. A METHOD OF MORDELL 268 4. EXISTENCE OF AUTOMORPHS 279 5. ISOLATION
THEOREMS 286 6. APPLICATIONS OF ISOLATION 295 7. AN INFINITY OF
SOLUTIONS 298 8. LOCAL METHODS 301 CHAPTER XI. INHOMOGENEOUS PROBLEMS
303 1. INTRODUCTION 303 2. CONVEX SETS 309 3. TRANSFERENCE THEOREMS FOR
CONVEX SETS 313 4. THE PRODUCT OF N LINEAR FORMS 322 APPENDIX 332
REFERENCES 334 INDEX 343 |
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| dewey-search | 512/.75 21 |
| dewey-sort | 3512 275 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Reprint of the 1971 ed. |
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| spelling | Cassels, John W. S. 1922-2015 Verfasser (DE-588)105102059 aut An introduction to the geometry of numbers J. W. S. Cassels Reprint of the 1971 ed. Berlin [u.a.] Springer 1997 VII, 344 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Classics in mathematics Auch als: Grundlehren der mathematischen Wissenschaften ; Vol. 99 Literaturverz. S. 334 - 343 Geometry of numbers Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Arithmetik (DE-588)4002919-0 gnd rswk-swf Geometrie der Zahlen (DE-588)4227477-1 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Arithmetik (DE-588)4002919-0 s Geometrie (DE-588)4020236-7 s DE-604 Geometrie der Zahlen (DE-588)4227477-1 s Zahlentheorie (DE-588)4067277-3 s 2\p DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016833947&sequence=000001&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 | Cassels, John W. S. 1922-2015 An introduction to the geometry of numbers Geometry of numbers Zahlentheorie (DE-588)4067277-3 gnd Arithmetik (DE-588)4002919-0 gnd Geometrie der Zahlen (DE-588)4227477-1 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4002919-0 (DE-588)4227477-1 (DE-588)4020236-7 (DE-588)4113937-9 |
| title | An introduction to the geometry of numbers |
| title_auth | An introduction to the geometry of numbers |
| title_exact_search | An introduction to the geometry of numbers |
| title_exact_search_txtP | An introduction to the geometry of numbers |
| title_full | An introduction to the geometry of numbers J. W. S. Cassels |
| title_fullStr | An introduction to the geometry of numbers J. W. S. Cassels |
| title_full_unstemmed | An introduction to the geometry of numbers J. W. S. Cassels |
| title_short | An introduction to the geometry of numbers |
| title_sort | an introduction to the geometry of numbers |
| topic | Geometry of numbers Zahlentheorie (DE-588)4067277-3 gnd Arithmetik (DE-588)4002919-0 gnd Geometrie der Zahlen (DE-588)4227477-1 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Geometry of numbers Zahlentheorie Arithmetik Geometrie der Zahlen Geometrie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016833947&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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