On the average growth exponent for beta-expansions

Nikita Sidorov

Let $\be\in(1,2)$. Each $x\in I_\be:=[0,\frac{1}{\be-1}]$ can be represented in the form \[ x=\sum_{k=1}^\infty a_k\be^{-k}, \] where $a_k\in \{0,1\}$ for all $k$ (a $\be$-expansion…