Joint distribution in residue classes of the base-$q$ and Ostrowski digital sums

Divyum Sharma

Let $q$ be an integer $\ge 2$ and let $S_q(n)$ denote the sum of digits of $n$ in base $q$. For \[ α=[0;\overline{1,m}],\ m\geq 2, \] let $S_{\alpha }(n)$ denote the sum of digits in the…