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V.I. Bernik and M.M. Dodson Metric Diophantine Approximation on Manifolds Cambridge University Press. 1999. 172 pages.
In English. Hardback Published by Cambridge University Press, Cambridge, United Kingdom.
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The book written by V.I. Bernik, the Institute of Mathematics of the National Academy of Sciences of Belarus (Minsk, Belarus), and M.M. Dodson, Department of Mathematics University of York (York, United Kingdom), is concerned with Diophantine approximation on smooth manifolds embedded in Euclidean space. 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 Khintohine-type theorems and with the Hausdorff dimension of the associated null sets. After setting out the necessary background material, a full discussion of Hausdorff dimension and its uses in Diophantine approximation is given. A wide range of techniques from the number theory 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 p-adic case is briefly considered, and the book is concluded with a chapter on some applications of metric Diophantine approximation. The book is aimed to all researchers with an interest in Diophantine approximation.
Please visit the Cambridge University Press' web page Metric Diophantine Approximation on Manifolds to find some other details about the book.
Publisher's Mailing Address: The Pitt Building, Trumpington Street, Cambridge, United Kingdom
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