On the asymptotic behaviour of the correlation measure of sum-of-digits function in base 2

Jordan Emme, Alexander Prikhod'Ko

Let $s\_2(x)$ denote the number of digits "$1$" in a binary expansion of any $x\in \mathbb{N}$. We study the mean distribution $\mu \_a$ of the quantity $s\_2(x+a)-s\_2(x)$ for a fix…