{
  "abstract": "We derive a recurrence for logarithmically weighted Möbius sums by combining Möbius inversion with the Euler-Maclaurin summation formula. Consequently, starting from estimates of orders zero, one and two, we obtain polynomial approximations for these sums for every nonnegative integer exponent of $\\log$. We then extend these estimates to sums with coprimality conditions via a convolution identity and to sums weighted by the reciprocal of the sum-of-divisors function. We also study the nonnegativity of the latter sums for every positive integer logarithmic order, establishing that they never change sign.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17720",
  "author_total": 1,
  "authors": [
    {
      "name": "Sebastian Zuniga Alterman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7tpk2v37bvzbk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17720",
  "fulltext_url": null,
  "id": "7tpk2v37bvzbk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17720",
  "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": "W7221786811",
  "pdf_url": "https://arxiv.org/pdf/2610.17720",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7tpk2v37bvzbk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.17720",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17720"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A recurrence in logarithmic Möbius sums with coprimality conditions via Euler--Maclaurin",
  "title_text": "A recurrence in logarithmic Möbius sums with coprimality conditions via Euler--Maclaurin",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/7tpk2v37bvzbk",
  "venue": "arXiv",
  "versions": []
}