{
  "abstract": "We study the growth of the number of invisible lattice points along powers of quadratic polynomials. Let $f(x)=Ax^2+Bx+C\\in\\mathbb{Z}[x]$ have a positive leading coefficient and nonzero discriminant, and let $F(x)=f(x)^m$ with $m\\geq 2$. For $m\\geq 3$ we prove that the number of invisible lattice points in $[1,N]^2$ has order $N\\log N$, and when $m=2$ the number of invisible lattice points satisfies $N\\log N \\ll_F\\#\\mathrm{Invisible}_F(N)\\ll_F N(\\log N)^4$. These estimates refine a previous result of the authors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05027",
  "author_total": 2,
  "authors": [
    {
      "name": "Abraham Lobsenz"
    },
    {
      "name": "Tristan Phillips"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ba7w553rerv09.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05027",
  "fulltext_url": null,
  "id": "ba7w553rerv09",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05027",
  "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": "W7211881685",
  "pdf_url": "https://arxiv.org/pdf/2609.05027",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ba7w553rerv09.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05027",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05027"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Lattice point visibility along powers of quadratic polynomials",
  "title_text": "Lattice point visibility along powers of quadratic polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/ba7w553rerv09",
  "venue": "arXiv",
  "versions": []
}