{
  "abstract": "We study the distribution of monogenic integral binary cubic forms $f(x,y)$ with bounded discriminant and bounded monogenizer inside a fundamental domain for the action of $\\mathrm{GL}_2(\\mathbb{Z})$ on the space of real binary cubic forms. We show that when the monogenizer for $f$ is $[\\pm1:0]$ (i.e., $f(\\pm1,0)=1$), the corresponding set is fully concentrated in the cusp. We also prove a complementary result, namely, that when the monogenizers $[\\pm1:0]$ (with height bounded in terms of the discriminant bound) are excluded, the resulting set has no escape of mass to the cusp. However, we surprisingly show that despite this non-escape of mass, the points in the fundamental domain are not equidistributed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33027",
  "author_total": 1,
  "authors": [
    {
      "name": "Petros Ploumidis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aryjs4c5kxtfy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33027",
  "fulltext_url": null,
  "id": "aryjs4c5kxtfy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33027",
  "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|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214782241",
  "pdf_url": "https://arxiv.org/pdf/2609.33027",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aryjs4c5kxtfy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33027",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33027"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Escape and Non-Escape of Mass for Monogenic Binary Cubic Forms",
  "title_text": "Escape and Non-Escape of Mass for Monogenic Binary Cubic Forms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/aryjs4c5kxtfy",
  "venue": "arXiv",
  "versions": []
}