{
  "abstract": "Using the \\emph{compression} method, we prove an inequality related to the Gauss circle problem. Let $\\mathcal{N}_r$ denote the number of integral points in a circle of radius $r>0$. We have $$ 2r^2\\bigg(1+\\frac{1}{4}\\sum \\limits_{1\\leq k\\leq \\lfloor \\frac{\\log r}{\\log 2}\\rfloor}\\frac{1}{2^{2k-2}}\\bigg)+O(\\frac{r}{\\log r}) \\leq \\mathcal{N}_r \\leq 8r^{2}\\bigg(1+\\sum \\limits_{1\\leq k\\leq \\lfloor \\frac{\\log r}{\\log 2}\\rfloor}\\frac{1}{2^{2k-2}}\\bigg)+O(\\frac{r}{\\log r}) $$ for all $r>1$. This implies that the error function $E(r)$ of the counting function $\\mathcal{N}_r\\ll r^{1-\\epsilon}$ for any $\\epsilon>0.$",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Theophilus Agama"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/35z88ezf98fqm.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "35z88ezf98fqm",
  "issns": [],
  "landing_url": "https://hal.science/hal-05777107v1",
  "language": "en",
  "licence": "CC-BY-ND-4.0",
  "licence_label": "CC BY-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05777107/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/35z88ezf98fqm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:47Z",
      "native_id": "hal-05777107",
      "source": "hal",
      "url": "https://hal.science/hal-05777107v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "ON THE GAUSS CIRCLE PROBLEM",
  "title_text": "ON THE GAUSS CIRCLE PROBLEM",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:47Z",
  "url": "https://research.draconitic.com/paper/35z88ezf98fqm",
  "venue": "HAL",
  "versions": []
}