An introduction to diophantine approximation:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Cambridge
Univ. Press
1965
|
Ausgabe: | Reprinted |
Schriftenreihe: | Cambridge tracts in mathematics and mathematical physics
45 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | VIII, 168 S. |
Internformat
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245 | 1 | 0 | |a An introduction to diophantine approximation |c by J. W. S. Cassels |
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300 | |a VIII, 168 S. | ||
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490 | 1 | |a Cambridge tracts in mathematics and mathematical physics |v 45 | |
650 | 4 | |a Diophantische Approximation | |
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Datensatz im Suchindex
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adam_text | CONTENTS
Preface page vii
Notation ix
Chapter I. homogeneous approximation
1 Introduction 1
2 The continued fraction process 2
3 Equivalence 8
4 Application to approximations 11
5 Simultaneous approximation 13
Chapter II. the maeioff chain
1 Introduction 18
2 Indefinite binary quadratic forms 20
3 A Diophantine equation 27
4 The Markoff forms 31
5 The Markoff chain for forms 39
6 The Markoff chain for approximations 41
Chapter III. inhomogeneous approximation
1 Introduction 45
2 The 1 dimensional case 46
3 A negative result 51
4 Linear independence over the rationals 52
5 Simultaneous approximation (Kronecker s theorem) 53
Chapter IV. uniform distribution
1 Introduction 60
2 Definition of discrepancy 61
3 Uniform distribution for linear forms 64
4 Weyl s criteria 65
5 Consequences of Weyl s criteria 71
Chapter V. transference theorems
1 Introduction 75
2 Transference between two homogeneous problems 76
3 Application to simultaneous approximations 79
vi CONTENTS
4 Transference between homogeneous and inhomo
geneous problems page 80
5 A direct converse to Theorem V 84
6 Application to inhomogeneous approximation 85
7 Regular and singular systems 92
8 A quantitative Kronecker s theorem 97
9 Successive minima 99
Chapter VI. rational approximation to
ALGEBRAIC NUMBERS. ROTH S THEOREM
1 Introduction 103
2 Preliminaries 104
3 Construction of R(xv ..., xm) 106
4 Behaviour of R at rational points near (£,...,£) 109
5 Behaviour at rational points of a polynomial with
integer coefficients 111
6 Proof of Theorem I 117
Chapter VII. metrical theory
1 Introduction 120
2 The convergence case (w= 1) 121
3 Two lemmas 122
4 Proof of Theorem II (divergence, n = 1) 123
5 Some more lemmas 125
6 Proof of Theorem I (divergence, n = 1) 127
7 The case w 2 131
Chapter VIII. the pisot vijayaraghavan numbers
1 Introduction 133
2 Proof of Theorem I 134
3 Proof of Theorem II 137
4 Proof of Theorem III 141
A Note on Developments since 1956 145
Appendix A. Bases in certain Modules 147
Appendix B. Tools from the Geometry of Numbers 150
Appendix C. Gauss s Lemma 161
Bibliography 163
Index of Definitions 170
|
any_adam_object | 1 |
author | Cassels, John W. S. 1922-2015 |
author_GND | (DE-588)105102059 |
author_facet | Cassels, John W. S. 1922-2015 |
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author_sort | Cassels, John W. S. 1922-2015 |
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building | Verbundindex |
bvnumber | BV007114757 |
classification_rvk | SK 180 |
ctrlnum | (OCoLC)258457687 (DE-599)BVBBV007114757 |
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illustrated | Not Illustrated |
indexdate | 2024-07-09T16:55:50Z |
institution | BVB |
language | English |
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owner | DE-355 DE-BY-UBR DE-29T DE-83 DE-188 |
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physical | VIII, 168 S. |
publishDate | 1965 |
publishDateSearch | 1965 |
publishDateSort | 1965 |
publisher | Univ. Press |
record_format | marc |
series | Cambridge tracts in mathematics and mathematical physics |
series2 | Cambridge tracts in mathematics and mathematical physics |
spelling | Cassels, John W. S. 1922-2015 Verfasser (DE-588)105102059 aut An introduction to diophantine approximation by J. W. S. Cassels Reprinted Cambridge Univ. Press 1965 VIII, 168 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics and mathematical physics 45 Diophantische Approximation Diophantische Approximation (DE-588)4135760-7 gnd rswk-swf Diophantische Approximation (DE-588)4135760-7 s DE-604 Cambridge tracts in mathematics and mathematical physics 45 (DE-604)BV001887938 45 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004531734&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Cassels, John W. S. 1922-2015 An introduction to diophantine approximation Cambridge tracts in mathematics and mathematical physics Diophantische Approximation Diophantische Approximation (DE-588)4135760-7 gnd |
subject_GND | (DE-588)4135760-7 |
title | An introduction to diophantine approximation |
title_auth | An introduction to diophantine approximation |
title_exact_search | An introduction to diophantine approximation |
title_full | An introduction to diophantine approximation by J. W. S. Cassels |
title_fullStr | An introduction to diophantine approximation by J. W. S. Cassels |
title_full_unstemmed | An introduction to diophantine approximation by J. W. S. Cassels |
title_short | An introduction to diophantine approximation |
title_sort | an introduction to diophantine approximation |
topic | Diophantische Approximation Diophantische Approximation (DE-588)4135760-7 gnd |
topic_facet | Diophantische Approximation |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004531734&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV001887938 |
work_keys_str_mv | AT casselsjohnws anintroductiontodiophantineapproximation |