{
  "abstract": "Let $D$ be the ring of $S$-integers in a global field and $\\widehat{D}$ its profinite completion. We propose a profinite version of the Bateman--Horn conjecture over $D$ and provide a first comparison with the classical one and its generalizations. Our approach is based on the new notion of procounting measure: a distribution on $\\widehat{D}$ which should be seen as a profinite analogue of the counting function for a subset of $\\mathbb{R}$. This allows us to deal with subsets of $\\widehat{D}$ having Haar measure $0$ (corresponding to density zero in $\\mathbb{R}$).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.29250",
  "author_total": 3,
  "authors": [
    {
      "name": "Luca Demangos"
    },
    {
      "name": "Ignazio Longhi"
    },
    {
      "name": "Francesco Maria Saettone"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7bvnnn99ssmex.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.29250",
  "fulltext_url": null,
  "id": "7bvnnn99ssmex",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.29250",
  "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": "W7166683456",
  "pdf_url": "https://arxiv.org/pdf/2606.29250",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7bvnnn99ssmex.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2606.29250",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.29250"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Procounting measures and the Bateman--Horn conjecture",
  "title_text": "Procounting measures and the Bateman--Horn conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/7bvnnn99ssmex",
  "venue": "arXiv",
  "versions": []
}