{
  "abstract": "For a vector of positive integers $\\mathbf{b} = (b_1,\\ldots,b_h)$ with $\\gcd(b_1,\\ldots,b_h) = 1$, we study sets $A \\subseteq \\mathbb{N}$ for which every sufficiently large integer has a bounded positive number of representations \\[ n = b_1 x_1 + \\cdots + b_h x_h \\qquad (x_1,\\ldots,x_h\\in A). \\] We prove that such a set exists for every binary vector $\\mathbf{b} \\neq (1,1)$, and for some general higher-dimensional families, including $\\mathbf{b} = (u_1, p^d u_2, \\ldots, p^{(h-1)d} u_h)$ where $p\\nmid u_1\\cdots u_h$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11848",
  "author_total": 1,
  "authors": [
    {
      "name": "Christian Táfula"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6w3nenrphakc6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11848",
  "fulltext_url": null,
  "id": "6w3nenrphakc6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11848",
  "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.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7212296789",
  "pdf_url": "https://arxiv.org/pdf/2609.11848",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6w3nenrphakc6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11848",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11848"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Bounded asymptotic bases for linear forms",
  "title_text": "Bounded asymptotic bases for linear forms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/6w3nenrphakc6",
  "venue": "arXiv",
  "versions": []
}