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arXiv · 2403.01957

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

Jean-François Burnol
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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 $A=ζ(2)/2$, $B = (3ζ(2)+ζ(3))/3$ and $C = (2ζ(2)+4ζ(3)+ζ(4))/4$.

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Jean-François Burnol. 2024-05-20. Sur l'asymptotique des sommes de Kempner pour de grandes bases. https://arxiv.org/abs/2403.01957

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