{
  "abstract": "Suppose a set of integers $A\\subseteq\\{1,\\dots,N\\}$ has no solutions to $a-a'=n\\lfloor\\sqrt[3]2n\\rfloor,$ for distinct $a,a'\\in A,$ and $n\\in \\mathbb{N}.$ We show that $|A|\\ll N^{1-c}$ for some absolute constant $c>0.$ To do this, we prove quantitative bounds on the van der Corput property for certain sets of bracket quadratics. This comes as a consequence of establishing exponential sum estimates for these sets, utilising a theorem of Green and Tao on the quantitative equidistribution of polynomial orbits on nilmanifolds, closely following the approach of Neale who went on to prove a Waring-type result. We also extend our result to differences avoiding a family of bracket polynomials (also known as generalised polynomials).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30078",
  "author_total": 1,
  "authors": [
    {
      "name": "Khalid Younis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ptns9cmpvs0r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30078",
  "fulltext_url": null,
  "id": "9ptns9cmpvs0r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30078",
  "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.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7204877447",
  "pdf_url": "https://arxiv.org/pdf/2608.30078",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ptns9cmpvs0r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30078",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30078"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Sets whose differences avoid a bracket quadratic",
  "title_text": "Sets whose differences avoid a bracket quadratic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/9ptns9cmpvs0r",
  "venue": "arXiv",
  "versions": []
}