Article contents
On the fractional parts of αn2 and βn
Published online by Cambridge University Press: 18 May 2009
Extract
We denote by ‖…‖ the distance to the nearest integer. Let α and β be real. W. M. Schmidt [5] proved that for ε > 0 and N>c1(ε) there is a natural number n such that
This extends a theorem of H. Heilbronn [4] and also sharpens a theorem of H. Davenport [3].
- Type
- Research Article
- Information
- Copyright
- Copyright © Glasgow Mathematical Journal Trust 1981
References
REFERENCES
- 2
- Cited by