{
  "abstract": "We obtain a Furstenberg-Sárközy-type result for sets $A\\subset [N]$ whose difference set $A-A$ does not contain the sum of $s$-many $k$-th powers of positive integers, with $k>1$ odd and $s>0$ even. Namely, we prove that such sets must satisfy a power-saving bound $|A| \\, \\ll \\, N^{1-\\frac1k\\min\\{s \\, σ_k, \\, 1/2\\}+ε}$ for any fixed $ε>0$, where $σ_k >0 $ is any admissible saving in a classical one-variable Weyl estimate. In particular, we can take $σ_k=\\max\\left\\{2^{1-k}, \\, \\frac{1}{k(k-1)}\\right\\}$ using the classical theory and the best currently available bounds for classical Weyl sums. A greedy construction produces a set $A\\subset[N]$ with $|A|\\gg N^{1-s/k}$ for which $A-A$ contains no sum of $s$-many positive $k$-th powers, so our power-saving bound is of the correct shape.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16595",
  "author_total": 4,
  "authors": [
    {
      "name": "Alexandros Kalogirou"
    },
    {
      "name": "Andrew Lott"
    },
    {
      "name": "Ákos Magyar"
    },
    {
      "name": "Akash Singha Roy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3zszkc83zsgny.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16595",
  "fulltext_url": null,
  "id": "3zszkc83zsgny",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16595",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7213394258",
  "pdf_url": "https://arxiv.org/pdf/2609.16595",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3zszkc83zsgny.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16595",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16595"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Furstenberg-Sárközy theorem for sums of an even number of odd powers",
  "title_text": "The Furstenberg-Sárközy theorem for sums of an even number of odd powers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/3zszkc83zsgny",
  "venue": "arXiv",
  "versions": []
}