On the Diophantine properties of lambda-expansions

Tomas Persson, Henry W. J. Reeve

For $\lambda \in (1/2,1)$ and $\alpha$, we consider sets of numbers $x$ such that for infinitely many $n$, $x$ is $2^{-\alpha n}$-close to some ${\sum }_{i=1}^n{\omega }_i{\lambda }^i$, where ${\omega }_i\in \{0,1\}$. Thes…