PreprintCC BY-SA 4.0arXiv
The modal expansion of Kempner sums
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≥1. 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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BibTeX
@misc{burnol2026modal,
title = {{The modal expansion of Kempner sums}},
author = {Jean-François Burnol},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31986},
eprint = {2609.31986},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31986},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - The modal expansion of Kempner sums
AU - Jean-François Burnol
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31986
UR - https://arxiv.org/abs/2609.31986
AB - 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≥1. 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.
ER -