
Metric Number Theory
Glyn Harman(Author)
Oxford University Press
Published on 11. June 1998
Book
Hardback
316 pages
978-0-19-850083-4 (ISBN)
Description
This book deals with the number-theoretic properties of almost all real numbers. It brings together many different types of result never covered within the same volume before, thus showing interactions and common ideas between different branches of the subject. It provides an indispensable compendium of basic results, important theorems and open problems. Starting from the classical results of Borel, Khintchine and Weyl, normal numbers, Diophantine approximation and uniform distribution are all discussed. Questions are generalized to higher dimensions and various non-periodic problems are also considered (for example restricting approximation to fractions with prime numerator and denominator). Finally, the dimensions of some of the exceptional sets of measure zero are considered.
Reviews / Votes
...very interesting book... * Peter Szusz, Zentralblatt MATH, Vol 1081 *More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Target group
Professional and scholarly
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 22 mm
Weight
640 gr
ISBN-13
978-0-19-850083-4 (9780198500834)
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Schweitzer Classification
Person
Professor G. Harman, School of Mathematics, Mathematics Institute, University of Wales Cardiff, Senghennydd Road, Cardiff, CF2 4YH, email: Harman@cf.ac.uk
Author
Professor of Pure MathematicsProfessor of Pure Mathematics, University of Wales, Cardiff
Content
Introduction ; 1. Normal numbers ; 2. Diophantine approximation ; 3. GCD sums with applications ; 4. Schmidt's method ; 5. Uniform distribution ; 6. Diophantine approximation with restricted numerator and denominator ; 7. Non-integer sequences ; 8. The integer parts of sequences ; 9. Diophantine approximation on manifolds ; 10. Hausdorff dimension of exceptional sets ; References ; Index