{
  "abstract": "Recently, Garvan and Sarma studied sums of non-overlined parts in overpartitions and partitions without repeated odd parts. In this paper, we study the corresponding statistic for overlined parts. We define $\\mathrm{OSOME}(n)$ as the sum of all odd overlined parts minus the sum of all even overlined parts in the overpartitions of $n$. We obtain a closed form for its generating function and use it to prove congruences by elementary $q$-series methods, the theory of half-integral weight modular forms, and known congruences for the overpartition function.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21361",
  "author_total": 2,
  "authors": [
    {
      "name": "Nayandeep Deka Baruah"
    },
    {
      "name": "Pankaj Gogoi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e3648sbqntdjh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21361",
  "fulltext_url": null,
  "id": "e3648sbqntdjh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21361",
  "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",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7213955663",
  "pdf_url": "https://arxiv.org/pdf/2609.21361",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e3648sbqntdjh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21361",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21361"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Difference of the Sum of All Odd and Even Overlined Parts of Overpartitions",
  "title_text": "Difference of the Sum of All Odd and Even Overlined Parts of Overpartitions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/e3648sbqntdjh",
  "venue": "arXiv",
  "versions": []
}