Diophantine approximations and value distribution theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1987
|
| Schriftenreihe: | Lecture notes in mathematics
1239 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 132 S. |
| ISBN: | 3540175512 0387175512 |
Internformat
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| 245 | 1 | 0 | |a Diophantine approximations and value distribution theory |c Paul Vojta |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Chapter 1. Heights and Integral Points 1
§1. Absolute values and the product formula 1
§2. Height functions 2
§3. Weil functions 7
§4. Integral points 10
Chapter 2. Diophantine Approximations 16
§1. Roth s theorem and its generalizations 16
§2. A reformulation of Schmidt s theorem 17
§3. Linear equations in units 19
§4. A theorem on integral points 21
§5. Arithmetic distance functions and Schmidt s theorem ... 24
§6. Exceptional hyperplanes 27
Chapter 3. A Correspondence with Nevanlinna Theory 30
§1. Introduction to Nevanlinna theory 31
§2. The correspondence in the case of one variable 33
§3. Defects 36
§4. The higher dimensional case 38
§5. Some examples 43
Chapter 4. Consequences of the Main Conjecture 46
§1. Degeneracy of integral points 46
§2. Integral points on abelian varieties 47
§3. Lang s conjectures on curvature and hyperbolicity 48
§4. Hall s conjecture 51
Chapter 5. The Ramification Term 57
§1. A generalized Chevalley Weil theorem 57
§2. The ramification term 61
§3. The P1 case of the General Conjecture 65
§4. Other remarks on the General Conjecture 68
§5. Examples: Fermat, abc, Hall, and Hall Lang Stark 70
§6. The (split) function field case 77
§7. The ramification term in the Conjecture using (1,1) forms . 80
Appendix ABC. The Masser Oesterle abc conjecture .... 84
X
Chapter 6. Approximation to Hyperplanes 89
§1. Successive minima 90
§2. Davenport s lemma 96
§3. Multilinear algebra 99
§4. The start of the algebraic proof 104
§5. A sketch of the analytic proof 112
§6. The remainder of the algebraic proof 118
§7. Conclusion 122
Bibliography 124
Index 130
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:17:33Z |
| institution | BVB |
| isbn | 3540175512 0387175512 |
| language | English |
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| physical | X, 132 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Vojta, Paul 1957- Verfasser (DE-588)111319668 aut Diophantine approximations and value distribution theory Paul Vojta Berlin [u.a.] Springer 1987 X, 132 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1239 Diophantische Approximation (DE-588)4135760-7 gnd rswk-swf Wertverteilungstheorie (DE-588)4137510-5 gnd rswk-swf Diophantische Approximation (DE-588)4135760-7 s Wertverteilungstheorie (DE-588)4137510-5 s DE-604 Lecture notes in mathematics 1239 (DE-604)BV000676446 1239 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000419074&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vojta, Paul 1957- Diophantine approximations and value distribution theory Lecture notes in mathematics Diophantische Approximation (DE-588)4135760-7 gnd Wertverteilungstheorie (DE-588)4137510-5 gnd |
| subject_GND | (DE-588)4135760-7 (DE-588)4137510-5 |
| title | Diophantine approximations and value distribution theory |
| title_auth | Diophantine approximations and value distribution theory |
| title_exact_search | Diophantine approximations and value distribution theory |
| title_full | Diophantine approximations and value distribution theory Paul Vojta |
| title_fullStr | Diophantine approximations and value distribution theory Paul Vojta |
| title_full_unstemmed | Diophantine approximations and value distribution theory Paul Vojta |
| title_short | Diophantine approximations and value distribution theory |
| title_sort | diophantine approximations and value distribution theory |
| topic | Diophantische Approximation (DE-588)4135760-7 gnd Wertverteilungstheorie (DE-588)4137510-5 gnd |
| topic_facet | Diophantische Approximation Wertverteilungstheorie |
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