{
  "abstract": "Motivated by the known derived set $[1,+\\infty)$ of multiple zeta-star values, we study finite multiple star harmonic sums and their infinite-depth limits. Divided differences give a cube-integral representation of their holomorphic interpolation on $\\mathrm{Re}(s)>0$, which agrees with the Kawashima functions after reversal of the index. The finite-depth interpolations converge locally uniformly in $s$ as the depth tends to infinity, uniformly over all positive integer index sequences on compact subsets. For real $s>1$, these limits define a bijection from the infinite positive integer indices onto $(1,s]$. For each admissible infinite index, they tend to the corresponding multiple zeta-star limit as $\\mathrm{Re}(s)\\to+\\infty$ with bounded imaginary part. For $\\mathrm{Re}(s)>1$, we prove strict separation of every ordered pair of finite indices and of every ordered pair of infinite indices: either the difference or the difference divided by $s$ has positive real part throughout this half-plane, with the choice fixed by the pair. In particular, both index maps are injective. The proof uses a summation principle for functions with positive real part, established through positive integral representations and explicit kernel estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.16627",
  "author_total": 1,
  "authors": [
    {
      "name": "Jiangtao Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b8ecq689fetrb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.16627",
  "fulltext_url": null,
  "id": "b8ecq689fetrb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.16627",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7164908917",
  "pdf_url": "https://arxiv.org/pdf/2606.16627",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b8ecq689fetrb.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:09Z",
      "native_id": "2606.16627",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.16627"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Divided differences and complex variations of multiple zeta-star values",
  "title_text": "Divided differences and complex variations of multiple zeta-star values",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:04Z",
  "url": "https://research.draconitic.com/paper/b8ecq689fetrb",
  "venue": "arXiv",
  "versions": []
}