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Mathematics > Number Theory
Title: Sur l'asymptotique des sommes de Kempner pour de grandes bases
(Submitted on 4 Mar 2024 (v1), last revised 26 Apr 2024 (this version, v2))
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 $C = (2\zeta(2)+4\zeta(3)+\zeta(4))/4$.
Submission history
From: Jean-François Burnol [view email][v1] Mon, 4 Mar 2024 11:52:15 GMT (11kb)
[v2] Fri, 26 Apr 2024 13:29:54 GMT (12kb)
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