{
  "abstract": "Authors, in an earlier work, proved that prime power subsequences of the polygonal numbers corresponding to $4$, $6$, $8$, and $10$ arise naturally as the numbers of $\\mathbb{F}_q$-rational points of certain double Danielewski surfaces. In this work, authors generalize the previous construction and give a new family of affine varieties over finite fields such that the number of $\\mathbb{F}_q$-rational points of these varieties give the prime power subsequence of every polygonal number sequence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32930",
  "author_total": 3,
  "authors": [
    {
      "name": "Sakshi Gupta"
    },
    {
      "name": "Anit Kuckian"
    },
    {
      "name": "Indranath Sengupta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/96s07bb405c0n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32930",
  "fulltext_url": null,
  "id": "96s07bb405c0n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32930",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223694837",
  "pdf_url": "https://arxiv.org/pdf/2610.32930",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/96s07bb405c0n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32930",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32930"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Rational Points on Affine Varieties over Finite Fields and Polygonal Number Sequences",
  "title_text": "Rational Points on Affine Varieties over Finite Fields and Polygonal Number Sequences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/96s07bb405c0n",
  "venue": "arXiv",
  "versions": []
}