{
  "abstract": "Let $E(X)=\\#\\{(a,b)\\in\\Z^2:a^2+b^2\\le X\\}-πX$. We prove that $E(X)=O_\\varepsilon(X^{209/670+\\varepsilon})$ for every $\\varepsilon>0$, uniformly for real $X\\ge4$. This breaks the $5/16$ threshold suggested by Huxley as a possible limit of the Bombieri--Iwaniec method at the time. The proof introduces two refinements: a cone distribution estimate that preserves separate fourth- and sixth-power contributions in the double large sieve, and an explicit inversion of Taylor-coefficient constraints that cancels the linear error in a pair-counting argument. These refinements, together with the Robert--Sargos and Watt spacing estimates and the Vinogradov mean value theorem, yield the improvement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21730",
  "author_total": 4,
  "authors": [
    {
      "name": "Xi Cen"
    },
    {
      "name": "Xitao Gao"
    },
    {
      "name": "Cheng Zhang"
    },
    {
      "name": "Junyong Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0t0p2j7wwec0q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21730",
  "fulltext_url": null,
  "id": "0t0p2j7wwec0q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21730",
  "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.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7222733598",
  "pdf_url": "https://arxiv.org/pdf/2610.21730",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0t0p2j7wwec0q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21730",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21730"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A New Bound for the Gauss Circle Problem",
  "title_text": "A New Bound for the Gauss Circle Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/0t0p2j7wwec0q",
  "venue": "arXiv",
  "versions": []
}