{
  "abstract": "For a positive integer $a$, let $b(a)$ be the smallest integer $b > a$ such that the denominator of $\\frac{1}{a} + \\frac{1}{a+1} + \\cdots + \\frac{1}{b}$ is smaller than the denominator of $\\frac{1}{a} + \\frac{1}{a+1} + \\cdots + \\frac{1}{b-1}$. Recently it was shown that the limit inferior $$\\liminf_{a \\to \\infty} \\left(\\frac{b(a) - a}{\\log a}\\right)$$ exists and is positive. Here we find its exact value.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00104",
  "author_total": 1,
  "authors": [
    {
      "name": "Wouter van Doorn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/39dr65wnf4ya2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00104",
  "fulltext_url": null,
  "id": "39dr65wnf4ya2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00104",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7206209601",
  "pdf_url": "https://arxiv.org/pdf/2609.00104",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/39dr65wnf4ya2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00104",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00104"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The shortest harmonic sums with decreasing denominator",
  "title_text": "The shortest harmonic sums with decreasing denominator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/39dr65wnf4ya2",
  "venue": "arXiv",
  "versions": []
}