Metric Number Theory
Seiten
1998
Oxford University Press (Verlag)
978-0-19-850083-4 (ISBN)
Oxford University Press (Verlag)
978-0-19-850083-4 (ISBN)
This book deals with the arithmetical properties of almost all real numbers. It brings together many different types of result (including normal numbers, Diophantine approximation and uniform distribution) never covered within the same volume before. By this approach interactions and common themes between different branches of the subject are revealed.
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.
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.
Professor G. Harman, School of Mathematics, Mathematics Institute, University of Wales Cardiff, Senghennydd Road, Cardiff, CF2 4YH, email: Harman@cf.ac.uk
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
| Erscheint lt. Verlag | 1.10.1998 |
|---|---|
| Reihe/Serie | London Mathematical Society Monographs ; 18 |
| Verlagsort | Oxford |
| Sprache | englisch |
| Maße | 162 x 242 mm |
| Gewicht | 619 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| ISBN-10 | 0-19-850083-1 / 0198500831 |
| ISBN-13 | 978-0-19-850083-4 / 9780198500834 |
| Zustand | Neuware |
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