On the sum-of-digits measures and Cusick's conjecture via stopped random walks

Dawid Tarłowski

Let $s(n)$ denote the number of ones in the binary expansion of a natural number $n\in \mathbb{N}$. For any $t\in \mathbb{N}$ and $d\in \mathbb{Z}$, let ${\mu }_t(d)$ denote the asymptotic…