{
  "abstract": "Fix a base $b\\ge2$ and a digit set $\\mathcal{D}\\subset\\{0,1,\\dots,b-1\\}$, and let $\\mathcal C_k$ be the set of integers in $[0,b^k)$ whose $k$ base-$b$ digits all lie in $\\mathcal D$. We study prime pairs and three-term arithmetic progressions in primes whose difference, or common difference, belongs to $\\mathcal C_k$. Under a natural digit non-resonance condition, we establish a localized Fourier criterion guaranteeing asymptotic formulae with explicit leading constants for both problems. Using a transfer-operator argument, we verify this criterion in explicit parameter ranges for several natural families of digit sets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05810",
  "author_total": 3,
  "authors": [
    {
      "name": "Rui Han"
    },
    {
      "name": "Yaghoub Rahimi"
    },
    {
      "name": "Fan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ate2kb6a7g26y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05810",
  "fulltext_url": null,
  "id": "ate2kb6a7g26y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05810",
  "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.CA"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7212073762",
  "pdf_url": "https://arxiv.org/pdf/2609.05810",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ate2kb6a7g26y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.05810",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05810"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Primes with Restricted-Digit Differences",
  "title_text": "Primes with Restricted-Digit Differences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/ate2kb6a7g26y",
  "venue": "arXiv",
  "versions": []
}