Power sums of digital sums (Q1066170)

Let \(e_ r(n)\), \(r\geq 0\), be the dyadic digits of the integer n. Set \(s(n)=\sum_{r}e_ r(n)\), and \(S_ d(N)=\sum_{n\leq N}s^ d(n)\). The author obtains asymptotic formulas, with error terms, for \(S_ d(N)\) as \(N\to +\infty\).