Metric Diophantine Approximation on Manifolds

Erscheinungsjahr 2012
ISBN: 978-0-521-43275-7
Verlag: Cambridge University Press

Buch, Englisch, Band 137, 184 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 429 g

Reihe: Cambridge Tracts in Mathematics

This 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.

Autoren/Hrsg.

Bernik, V. I.

Dodson, M. M.

Bernik, Vasilii Ivanovich

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

1. Diophantine approximation; 2. Khintchine-type manifolds; 3. Hausdorff measure and dimension; 4. Upper bounds; 5. Lower bounds for Hausdorff dimension; 6. p-adic Diophantine approximation; 7. Applications.