Sur l'asymptotique des sommes de Kempner pour de grandes bases

Abstract

Let $K$ be the sum of the reciprocals of the integers with no occurrence of the digit $b-1$ in base $b$. We show $K = b\log(b) - A/b - B/b^2-C/b^3+O(1/b^4)$ with $A=\zeta(2)/2$, $B = (3\zeta(2)+\zeta(3))/3$ and $C = (2\zeta(2)+4\zeta(3)+\zeta(4))/4$.