{
  "abstract": "For a fixed modulus h and residue class c, we study the logarithmic mass of primes p in a fixed power band for which the exponent of p in n! is congruent to c modulo h. We establish the asymptotic ((b-a)/h + o(1)) log(n!) for primes satisfying n^a < p <= n^b, where 0 <= a < b <= 1. The argument combines a fixed-order derivative estimate, Vaughan's identity, and finite Fourier approximation of a discontinuous valuation function. We also derive a necessary capacity condition for infinite families of solutions to polynomial-factorial equations P(x) = n!.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37460",
  "author_total": 1,
  "authors": [
    {
      "name": "Ma Yicen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7xc6a7c3pezqj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37460",
  "fulltext_url": null,
  "id": "7xc6a7c3pezqj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37460",
  "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.FA"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214977678",
  "pdf_url": "https://arxiv.org/pdf/2609.37460",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7xc6a7c3pezqj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37460",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37460"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weighted equidistribution of factorial prime valuations in fixed power bands",
  "title_text": "Weighted equidistribution of factorial prime valuations in fixed power bands",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/7xc6a7c3pezqj",
  "venue": "arXiv",
  "versions": []
}