{
  "abstract": "We prove that the bound \\[ \\max \\{ |16A|,|16f(A)| \\} \\gg_m |A|^{\\frac{3}{2}+\\frac{1}{162}} \\] holds for any polynomial $f$ with degree $m \\geq 2$ and any finite $A \\subset \\mathbb R$. This shows that the classical Jarník obstruction to growth beyond exponent $3/2$, which occurs for general strictly convex functions, cannot occur for polynomial functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15265",
  "author_total": 2,
  "authors": [
    {
      "name": "Michalis Kokkinos"
    },
    {
      "name": "Oliver Roche-Newton"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2gvz66nf2nfs2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15265",
  "fulltext_url": null,
  "id": "2gvz66nf2nfs2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15265",
  "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": "W7213250317",
  "pdf_url": "https://arxiv.org/pdf/2609.15265",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2gvz66nf2nfs2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15265",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15265"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Growth beyond exponent $3/2$ for convexity and iterated sum sets",
  "title_text": "Growth beyond exponent 3/2 for convexity and iterated sum sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/2gvz66nf2nfs2",
  "venue": "arXiv",
  "versions": []
}