{
  "abstract": "In this paper, we prove a conditional result that yields an asymptotic formula with an explicit main term and a power-saving error term for the generalized shifted ternary additive divisor sum $D_{\\mathcal{I},\\mathcal{J}}(X,1)=\\sum_{n \\leq X} τ_{\\mathcal{I}}(n) τ_{\\mathcal{J}}(n + 1)$, where $\\mathcal{I}=\\{α_1,α_2,α_3\\}$ and $\\mathcal{J} = \\{β_1, β_2, β_3\\}$, with $|α_i|, |β_i|\\leq δ$ for $i=1,2,3$, and $0<δ<1/44$. The proof of our main theorem relies on assuming an averaged level of distribution for the generalized ternary additive divisor function $τ_{\\mathcal{J}}$ in arithmetic progressions up to the level $2/3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10966",
  "author_total": 2,
  "authors": [
    {
      "name": "Alia Hamieh"
    },
    {
      "name": "Do Nhat Tan Vo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9bd5mkmv8y1aq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10966",
  "fulltext_url": null,
  "id": "9bd5mkmv8y1aq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10966",
  "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|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7221104649",
  "pdf_url": "https://arxiv.org/pdf/2610.10966",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9bd5mkmv8y1aq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10966",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10966"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Additive Sums of Generalized Shifted Ternary Divisor Functions",
  "title_text": "Additive Sums of Generalized Shifted Ternary Divisor Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/9bd5mkmv8y1aq",
  "venue": "arXiv",
  "versions": []
}