Metric number theory
著者
書誌事項
Metric number theory
（London Mathematical Society monographs, new ser.,
Clarendon Press , Oxford University Press, 1998
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注記
Includes bibliographical references (p. [280]-293)
Includes index
内容説明・目次
内容説明
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.
目次
- 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
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