Metric number theory
Author(s)
Bibliographic Information
Metric number theory
（London Mathematical Society monographs, new ser.,
Clarendon Press , Oxford University Press, 1998
Available at / 37 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC21:512.7/H2272070442778
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Note
Includes bibliographical references (p. [280]-293)
Includes index
Description and Table of Contents
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.
Table of Contents
- 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
by "Nielsen BookData"