Expansions in non-integer bases: lower, middle and top orders

Nikita Sidorov

Let $q\in (1,2)$; it is known that each $x\in [0,1/(q-1)]$ has an expansion of the form $x={\sum }_{n=1}^{\infty }{a}_n{q}^{-n}$ with $a_n\in \{0,1\}$. It was shown in \cite{EJK} that if $q<(\…