{
  "abstract": "It is shown that the random prime Dirichlet series $ X(s)=\\sum_{p\\in \\mathcal{P}}\\frac{ξ_p}{p^{s+1/2}} $ can be almost surely approximated by a Brownian motion, where $ \\{ξ_p\\}_{p\\ge 1} $ are independent and identically distributed random variables with zero mean and finite variance, and $ \\mathcal{P} $ is the set of prime numbers. As a consequence, the functional law of the iterated logarithm, limit laws of the iterated logarithm, and Chung's law of the iterated logarithm for $ X(s) $ are obtained. It is also shown that the random Dirichlet series $ Y(s)=\\sum_{k=2}^{\\infty} \\frac{(\\log k)^α}{k^{s+1/2}} $ with $ α=-1/2 $ admits the same approximation as $ X(s) $, and a direct relationship between $ X(s) $ and $ Y(s) $ with $ α=-1/2 $ is established. The strong invariance principle for $ Y(s) $ with $ α>-1/2 $ is also obtained.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18353",
  "author_total": 1,
  "authors": [
    {
      "name": "Li-Xin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dpzydzb2gkyck.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18353",
  "fulltext_url": null,
  "id": "dpzydzb2gkyck",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18353",
  "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.PR"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7221821328",
  "pdf_url": "https://arxiv.org/pdf/2610.18353",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dpzydzb2gkyck.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.18353",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18353"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Strong Invariance Principle for Random Dirichlet Series",
  "title_text": "Strong Invariance Principle for Random Dirichlet Series",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/dpzydzb2gkyck",
  "venue": "arXiv",
  "versions": []
}