Stolarsky's conjecture and the sum of digits of polynomial values

K. G. Hare, S. Laishram, T. Stoll

Let $s_q(n)$ denote the sum of the digits in the $q$-ary expansion of an integer $n$. In 1978, Stolarsky showed that $$\underset{n\to \infty }{\mathrm{liminf}}\frac{s_2(n^2)}{s_2(n)}=0.$$ He conj…