Metric diophantine approximation on manifolds:
This 1999 book is concerned with Diophantine approximation on smooth manifolds embedded in Euclidean space, and its aim is to develop a coherent body of theory comparable with that which already exists for classical Diophantine approximation. In particular, this book deals with Khintchine-type theor...
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1999
|
| Schriftenreihe: | Cambridge tracts in mathematics
137 |
| Links: | https://doi.org/10.1017/CBO9780511565991 |
| Zusammenfassung: | This 1999 book is concerned with Diophantine approximation on smooth manifolds embedded in Euclidean space, and its aim is to develop a coherent body of theory comparable with that which already exists for classical Diophantine approximation. In particular, this book deals with Khintchine-type theorems and with the Hausdorff dimension of the associated null sets. After setting out the necessary background material, the authors give a full discussion of Hausdorff dimension and its uses in Diophantine approximation. A wide range of techniques from the number theory arsenal are used to obtain the upper and lower bounds required, and this is an indication of the difficulty of some of the questions considered. The authors go on to consider briefly the p-adic case, and they conclude with a chapter on some applications of metric Diophantine approximation. All researchers with an interest in Diophantine approximation will welcome this book. |
| Umfang: | 1 Online-Ressource (xi, 172 Seiten) |
| ISBN: | 9780511565991 |
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| 100 | 1 | |a Bernik, V. I. | |
| 245 | 1 | 0 | |a Metric diophantine approximation on manifolds |c V.I. Bernik, M.M. Dodson |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 1999 | |
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| 490 | 1 | |a Cambridge tracts in mathematics |v 137 | |
| 520 | |a This 1999 book is concerned with Diophantine approximation on smooth manifolds embedded in Euclidean space, and its aim is to develop a coherent body of theory comparable with that which already exists for classical Diophantine approximation. In particular, this book deals with Khintchine-type theorems and with the Hausdorff dimension of the associated null sets. After setting out the necessary background material, the authors give a full discussion of Hausdorff dimension and its uses in Diophantine approximation. A wide range of techniques from the number theory arsenal are used to obtain the upper and lower bounds required, and this is an indication of the difficulty of some of the questions considered. The authors go on to consider briefly the p-adic case, and they conclude with a chapter on some applications of metric Diophantine approximation. All researchers with an interest in Diophantine approximation will welcome this book. | ||
| 700 | 1 | |a Dodson, M. M. | |
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| indexdate | 2025-03-03T11:58:04Z |
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| isbn | 9780511565991 |
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| spelling | Bernik, V. I. Metric diophantine approximation on manifolds V.I. Bernik, M.M. Dodson Cambridge Cambridge University Press 1999 1 Online-Ressource (xi, 172 Seiten) txt c cr Cambridge tracts in mathematics 137 This 1999 book is concerned with Diophantine approximation on smooth manifolds embedded in Euclidean space, and its aim is to develop a coherent body of theory comparable with that which already exists for classical Diophantine approximation. In particular, this book deals with Khintchine-type theorems and with the Hausdorff dimension of the associated null sets. After setting out the necessary background material, the authors give a full discussion of Hausdorff dimension and its uses in Diophantine approximation. A wide range of techniques from the number theory arsenal are used to obtain the upper and lower bounds required, and this is an indication of the difficulty of some of the questions considered. The authors go on to consider briefly the p-adic case, and they conclude with a chapter on some applications of metric Diophantine approximation. All researchers with an interest in Diophantine approximation will welcome this book. Dodson, M. M. Erscheint auch als Druck-Ausgabe 9780521432757 |
| spellingShingle | Bernik, V. I. Metric diophantine approximation on manifolds |
| title | Metric diophantine approximation on manifolds |
| title_auth | Metric diophantine approximation on manifolds |
| title_exact_search | Metric diophantine approximation on manifolds |
| title_full | Metric diophantine approximation on manifolds V.I. Bernik, M.M. Dodson |
| title_fullStr | Metric diophantine approximation on manifolds V.I. Bernik, M.M. Dodson |
| title_full_unstemmed | Metric diophantine approximation on manifolds V.I. Bernik, M.M. Dodson |
| title_short | Metric diophantine approximation on manifolds |
| title_sort | metric diophantine approximation on manifolds |
| work_keys_str_mv | AT bernikvi metricdiophantineapproximationonmanifolds AT dodsonmm metricdiophantineapproximationonmanifolds |