{
  "abstract": "For the Möbius-weighted quadratic form $T(N)=\\sum_{m,n\\leq N}μ(m)μ(n)(m,n)^2/(mn)$, we prove that $T(N)=cN+O_{\\varepsilon}(N^{2/3+\\varepsilon})$ for every $\\varepsilon>0$, where $c>0$ is given by an absolutely convergent series of finite Möbius sums multiplied by a convergent Euler product. The proof combines the classical Jordan-totient decomposition of the GCD kernel with a mean-value estimate that is uniform in a coprimality parameter. Grouping the resulting squares according to $\\lfloor N/d\\rfloor$ gives the error term and a nonnegative series for $c$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00525",
  "author_total": 1,
  "authors": [
    {
      "name": "Ahmadreza Azimifard"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c0s0g9hbxjvgm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00525",
  "fulltext_url": null,
  "id": "c0s0g9hbxjvgm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00525",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00525",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c0s0g9hbxjvgm.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00525",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00525"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A power-saving asymptotic for a Möbius-weighted GCD quadratic form",
  "title_text": "A power-saving asymptotic for a Möbius-weighted GCD quadratic form",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/c0s0g9hbxjvgm",
  "venue": "arXiv",
  "versions": []
}