Article contents
ON THE DIOPHANTINE PROPERTIES OF λ-EXPANSIONS
Published online by Cambridge University Press: 05 December 2012
Abstract
For and α, we consider sets of numbers x such that for infinitely many n, x is 2−αn-close to some ∑ ni=1ωiλi, where ωi∈{0,1}. These sets are in Falconer’s intersection classes for Hausdorff dimension s for some s such that −(1/α)(log λ /log 2 )≤s≤1/α. We show that for almost all , the upper bound of s is optimal, but for a countable infinity of values of λ the lower bound is the best possible result.
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright © University College London 2012
References
- 4
- Cited by