{
  "abstract": "A central problem in zero-sum theory is to determine the Davenport constant of a finite abelian group. For a finite abelian group $G\\cong C_{n_1}\\oplus\\cdots\\oplus C_{n_r}$, with $1<n_1\\mid\\cdots\\mid n_r$, let $\\mathsf D(G)$ be the least integer $t$ such that every sequence of $t$ elements of $G$ contains a nonempty zero-sum subsequence, and denote $\\mathsf D^*(G):= 1+\\sum_{i=1}^r(n_i-1)$. The standard construction shows that $\\mathsf D(G)\\ge\\mathsf D^*(G)$. Equality holds for several important classes of groups but fails in general, and even the question whether $\\mathsf D(G)/\\mathsf D^*(G)$ is bounded by an absolute constant remains open. In this paper, we prove the upper bound \\[ \\mathsf D(G)<4.86\\,\\exp(G)\\frac{\\log|G|}{\\log\\exp(G)} \\] for every finite abelian group. When $|G|$ is large compared with $\\exp(G)$, it improves the previous classical upper bound by a factor of order $\\log\\exp(G)$. We also prove that, for almost all finite abelian groups (counting isomorphism classes by order), \\[ \\mathsf D(G)\\sim\\exp(G)\\frac{\\log|G|}{\\log\\exp(G)}\\sim\\mathsf D^*(G). \\] We also study the difference $\\mathsf D(G)-\\mathsf D^*(G)$: for every function $L$ with $L(x)\\to\\infty$, almost all groups satisfy $\\mathsf D(G)-\\mathsf D^*(G)\\le L(\\mathsf D^*(G))$. However, for every fixed $C\\ge0$, the groups with $\\mathsf D(G)-\\mathsf D^*(G)>C$ have positive lower density.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15102",
  "author_total": 2,
  "authors": [
    {
      "name": "Dongchun Han"
    },
    {
      "name": "Hanbin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fjghxm2sq7wj1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15102",
  "fulltext_url": null,
  "id": "fjghxm2sq7wj1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15102",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7221813771",
  "pdf_url": "https://arxiv.org/pdf/2610.15102",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fjghxm2sq7wj1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15102",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15102"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Davenport Constants of Finite Abelian Groups",
  "title_text": "Davenport Constants of Finite Abelian Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/fjghxm2sq7wj1",
  "venue": "arXiv",
  "versions": []
}