{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31986",
  "author_total": 1,
  "authors": [
    {
      "name": "Jean-François Burnol"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8bz79p47s62b6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31986",
  "fulltext_url": null,
  "id": "8bz79p47s62b6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31986",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214753715",
  "pdf_url": "https://arxiv.org/pdf/2609.31986",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8bz79p47s62b6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.31986",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31986"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The modal expansion of Kempner sums",
  "title_text": "The modal expansion of Kempner sums",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/8bz79p47s62b6",
  "venue": "arXiv",
  "versions": []
}