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arXiv · 2609.31986

The modal expansion of Kempner sums

Jean-François Burnol
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Abstract

This is a continuation of the author's earlier paper Block-count constrained harmonic sums: spectral expansion and block-directed Euler--Maclaurin. We presented in that reference the modal expansion of block-Irwin sums $I(b,w,k)$ for $k\geq1$. The case $k=0$ was fully developed when $w$ is a single digit, but it was presented only as a very short result summary for $w$ a multi-digit block. Although the framework is already completely exposed in the earlier paper, the case $k=0$ requires adding a separate, dedicated discussion, which is provided here.

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Jean-François Burnol. 2026-09-25. The modal expansion of Kempner sums. https://arxiv.org/abs/2609.31986

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