{
  "abstract": "Let $f:\\mathbb{Z}\\to\\mathbb{C}$ be a multiplicative function. Assume there exist integers $a>1$ and $d>1$ such that $(a,d)=1$ and let $\\mathcal{P}_{a,d}=\\{a+kd:k\\in\\mathbb{Z}\\}$. Under mild extra conditions on $d$ and $f(a)$, we prove that $f(n)=nχ(n)$ for all $n$ outside an explicit exceptional set depending on $d$, and some Dirichlet character $χ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Comb. Number Th. 15 (2026) 217-226",
  "arxiv": "2607.22363",
  "author_total": 2,
  "authors": [
    {
      "name": "Crystel Bujold"
    },
    {
      "name": "Isabelle Taylor-Daoust"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fm01veh4313vx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.22363",
  "fulltext_url": null,
  "id": "fm01veh4313vx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.22363",
  "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/2607.22363",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fm01veh4313vx.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:28Z",
      "native_id": "2607.22363",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.22363"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Playing with additivity conditions in multiplicative functions",
  "title_text": "Playing with additivity conditions in multiplicative functions",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/fm01veh4313vx",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.2140/cnt.2026.15.217",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}