Diophantine approximations and diophantine equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1991
|
| Series: | Lecture notes in mathematics
1467 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 209 - 215 |
| Physical Description: | VIII, 217 S. graph. Darst. |
| ISBN: | 354054058X 038754058X |
Staff View
MARC
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| 100 | 1 | |a Schmidt, Wolfgang M. |d 1933- |e Verfasser |0 (DE-588)136169627 |4 aut | |
| 245 | 1 | 0 | |a Diophantine approximations and diophantine equations |c Wolfgang M. Schmidt |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1991 | |
| 300 | |a VIII, 217 S. |b graph. Darst. | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1467 | |
| 500 | |a Literaturverz. S. 209 - 215 | ||
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Record in the Search Index
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| adam_text | Table of Contents
Chapter Page
I. Siegel s Lemmas and Heights 1
1. Siegel s Lemma 1
2. Geometry of Numbers 3
3. Lattice Packings 7
4. Siegel s Lemma Again 9
5. Grassman Algebra 11
6. Absolute Values 18
7. Heights in Number Fields 22
8. Heights of Subspaces 28
9. Another Version of Siegel s Lemma 32
II. Diophantine Approximation 34
1. Dirichlet s Theorem and Liouville s Theorem 34
2. Roth s Theorem 38
3. Construction of a Polynomial 42
4. Upper Bounds for the Index 45
5. Estimation of Volumes 48
6. A Version of Roth s Theorem 49
7. Proof of the Main Theorems 52
8. Counting Good Rational Approximations 57
9. The Number of Good Approximations to Algebraic Numbers 63
10. A Generalization of Roth s Theorem 69
III. The Thue Equation 73
1. Main Result 73
2. Preliminaries 76
3. More on the connection between Thue s Equation and
Diophantine Approximation 83
4. Large Solutions 85
5. Small Solutions 86
6. How to Go From F(x) = 1 to F(x) = m 91
7. Thue Equations with Few Coefficients 99
8. The Distribution of the Roots of Sparse Polynomials 100
9. The Angular Distribution of Roots 106
10. On Trinomials 111
11. Roots of / close to | 116
12. Proof of 7A 119
13. Generalizations of the Thue Equation 124
VIII
Table of Contents (cont.)
Chapter Page
IV. 5 unit Equations and Hyperelliptic Equations 127
1. 5 unit Equations and Hyperelliptic Equations 127
2. Evertse s Bound 129
3. More on 5 unit Equations 134
4. Elliptic, Hyperelliptic, and Superelliptic Equations 137
5. The Number of Solutions of Elliptic, Hyperelliptic, and
Superelliptic Equations 142
6. On Elliptic Curves 147
7. The Rank of Cubic Thue Curves 159
8. Lower Bounds for the Number of Solutions of Cubic Thue Equations .. 163
9. Upper Bounds for Rational Points on Certain Elliptic Equations
in terms of the Mordell Weil Rank 165
10. Isogenies 169
11. Upper Bounds on Cubic Thue Equations in Terms of the
Mordell Weil Rank 173
12. More General Results 175
V. Diophantine Equations in More Than Two Variables 176
1. The Subspace Theorem 176
2. Generalized 5 unit Equations 180
3. Norm Form Equations 182
4. A Reduction 186
5. An Application of the Geometry of Numbers 188
6. Products of Linear Forms 192
7. A Generalized Gap Principle 193
8. Small Solutions 199
9. Large Solutions 200
10. Proof of Theorem 3B 203
Epilogue. The a6c conjecture 205
Bibliography 209
Index of Symbols 216
|
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| ctrlnum | (OCoLC)260187449 (DE-599)BVBBV004727857 |
| discipline | Mathematik |
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| id | DE-604.BV004727857 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:16:47Z |
| institution | BVB |
| isbn | 354054058X 038754058X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002907174 |
| oclc_num | 260187449 |
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| physical | VIII, 217 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Schmidt, Wolfgang M. 1933- Verfasser (DE-588)136169627 aut Diophantine approximations and diophantine equations Wolfgang M. Schmidt Berlin [u.a.] Springer 1991 VIII, 217 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1467 Literaturverz. S. 209 - 215 Diophantische Gleichung (DE-588)4012386-8 gnd rswk-swf Diophantische Approximation (DE-588)4135760-7 gnd rswk-swf Diophantische Approximation (DE-588)4135760-7 s DE-604 Diophantische Gleichung (DE-588)4012386-8 s Lecture notes in mathematics 1467 (DE-604)BV000676446 1467 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002907174&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schmidt, Wolfgang M. 1933- Diophantine approximations and diophantine equations Lecture notes in mathematics Diophantische Gleichung (DE-588)4012386-8 gnd Diophantische Approximation (DE-588)4135760-7 gnd |
| subject_GND | (DE-588)4012386-8 (DE-588)4135760-7 |
| title | Diophantine approximations and diophantine equations |
| title_auth | Diophantine approximations and diophantine equations |
| title_exact_search | Diophantine approximations and diophantine equations |
| title_full | Diophantine approximations and diophantine equations Wolfgang M. Schmidt |
| title_fullStr | Diophantine approximations and diophantine equations Wolfgang M. Schmidt |
| title_full_unstemmed | Diophantine approximations and diophantine equations Wolfgang M. Schmidt |
| title_short | Diophantine approximations and diophantine equations |
| title_sort | diophantine approximations and diophantine equations |
| topic | Diophantische Gleichung (DE-588)4012386-8 gnd Diophantische Approximation (DE-588)4135760-7 gnd |
| topic_facet | Diophantische Gleichung Diophantische Approximation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002907174&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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