{
  "abstract": "Let $m,n\\geq2$ be integers. We study the least exponent $t_{m,n}$ such that the $m$-fold additive energy of any subset $A$ of the discrete cube $\\{0,1,\\cdots,n-1\\}^d$ in any dimension $d$ satisfies $E_m(A)\\leq |A|^{t_{m,n}}$. For every fixed $m$, we obtain the asymptotic formula $$ t_{m,n}=2m-1-(1+o(1))\\log_n \\frac{(2m-1)^{m-1/2}}{(2m)^{m-1}} \\qquad(n\\to\\infty). $$ For $m=2$, this gives $$ t_{2,n} = 3 - (1+o(1)) \\log_n\\frac{3\\sqrt{3}}{4}, $$ proving a conjecture of the first author.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07490",
  "author_total": 2,
  "authors": [
    {
      "name": "Xuancheng Shao"
    },
    {
      "name": "Yu-Chen Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eq7nrwj297e3q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07490",
  "fulltext_url": null,
  "id": "eq7nrwj297e3q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07490",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7220988511",
  "pdf_url": "https://arxiv.org/pdf/2610.07490",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eq7nrwj297e3q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07490",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07490"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Higher additive energies on discrete cubes",
  "title_text": "Higher additive energies on discrete cubes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/eq7nrwj297e3q",
  "venue": "arXiv",
  "versions": []
}