{
  "abstract": "Heretofore, the second and third author conjectured that the D'Arcais polynomials, related to the coefficients of the powers of the Dedekind $η$-function, are Hurwitz polynomials except for a root at the origin. We show that this does in fact not hold for a positive proportion of all natural numbers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.18842",
  "author_total": 5,
  "authors": [
    {
      "name": "Steven Charlton"
    },
    {
      "name": "Bernhard Heim"
    },
    {
      "name": "Markus Neuhauser"
    },
    {
      "name": "Johann Stumpenhusen"
    },
    {
      "name": "Robert Tröger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bvaj2b7s1gjyz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.18842",
  "fulltext_url": null,
  "id": "bvaj2b7s1gjyz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.18842",
  "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": "W7203942125",
  "pdf_url": "https://arxiv.org/pdf/2608.18842",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bvaj2b7s1gjyz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2608.18842",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.18842"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Positive Proportion of the Reduced D'Arcais Polynomials is not Hurwitz",
  "title_text": "A Positive Proportion of the Reduced D'Arcais Polynomials is not Hurwitz",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/bvaj2b7s1gjyz",
  "venue": "arXiv",
  "versions": []
}