{
  "abstract": "Let $Q=\\{q_n\\}_{n\\geq1}$ be a sequence of integers with $q_n\\geq2$ for every $n\\geq1$. Every $x\\in[0,1)$ admits a Cantor series expansion of the form $$ x = \\frac{\\varepsilon_1(x)}{q_1} + \\frac{\\varepsilon_2(x)}{q_1q_2} +\\cdots+ \\frac{\\varepsilon_n(x)}{q_1q_2\\cdots q_n} +\\cdots.$$In this paper, we study exact approximation of real numbers by the $n$-th partial sums of their Cantor series expansions. More precisely, for a non-increasing function $ψ:\\mathbb{N}\\to(0,\\infty)$ satisfying $ψ(n)\\to0$, let $E_c(ψ)$ be the set of points that are $ψ$-approximable by their $n$-th partial sums but are not $bψ$-approximable for any $0<b<1$. We determine the Hausdorff dimension of $E_c(ψ)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.30435",
  "author_total": 2,
  "authors": [
    {
      "name": "Wanjin Cheng"
    },
    {
      "name": "Xinyun Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/83b0jgm0g85bv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.30435",
  "fulltext_url": null,
  "id": "83b0jgm0g85bv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.30435",
  "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",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7166651548",
  "pdf_url": "https://arxiv.org/pdf/2606.30435",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/83b0jgm0g85bv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2606.30435",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.30435"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Exact approximation order of real numbers in Cantor series expansions",
  "title_text": "Exact approximation order of real numbers in Cantor series expansions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/83b0jgm0g85bv",
  "venue": "arXiv",
  "versions": []
}