{
  "abstract": "We study analogues over number fields and the probabilistic congruence input that enters averaged versions of this problem. We prove an asymptotic formula for the least common multiple of ideals in a fixed ray class, record local equidistribution estimates for random $S_n$-polynomials, and give a conditional reduction of the averaged higher degree problem to explicit dispersion and large prime collision estimates. We also formulate an individual quadratic number field analogue and reduce it to a prime ideal quadratic root equidistribution statement together with a geometric pair counting estimate. The Galois group counting input is updated using Bhargava's theorem over $\\mathbb Q$ and the determinant method estimates of https://arxiv.org/abs/2610.35030 .",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39911",
  "author_total": 1,
  "authors": [
    {
      "name": "Ilaria Viglino"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2xpfyj5dn5wtg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39911",
  "fulltext_url": null,
  "id": "2xpfyj5dn5wtg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39911",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39911",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2xpfyj5dn5wtg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39911",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39911"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Least common multiples of polynomial values: averaging, ray classes, and Galois statistics",
  "title_text": "Least common multiples of polynomial values: averaging, ray classes, and Galois statistics",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/2xpfyj5dn5wtg",
  "venue": "arXiv",
  "versions": []
}