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 $C=(2\zeta (2)+4\zeta (3)+\zeta (4))/4$.

arXiv comment11 pages, in French. v3 differs from v2 only via a largely rewritten introduction, added references, the use of one-half line spacing and a change of typeface