{
  "abstract": "Let $π$ be a spherical cuspidal $\\mathrm{GL}_3$ newform of prime level $N$ and trivial central character, and define $S(t,π)=π^{-1}\\arg L(1/2+\\textrm{i}t,π)$. Assuming the generalized Riemann hypothesis for $L(s,π)$, we establish an asymptotic formula for each fixed weighted moment of $S(t,π)$ as $N\\to\\infty$, for fixed $t>0$. Consequently, under the same weights, $S(t,π)/\\sqrt{\\log\\log N}$ converges in distribution to a centered Gaussian distribution of variance $1/(2π^2)$. The key input is a weighted orthogonality formula derived from the Kuznetsov formula of prime level.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23201",
  "author_total": 2,
  "authors": [
    {
      "name": "Qingfeng Sun"
    },
    {
      "name": "Hui Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/anjb3epyt0t2c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23201",
  "fulltext_url": null,
  "id": "anjb3epyt0t2c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23201",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7222977197",
  "pdf_url": "https://arxiv.org/pdf/2610.23201",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/anjb3epyt0t2c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23201",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23201"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A $\\mathrm{GL}_3$ level analog of Selberg's result for $S(t)$",
  "title_text": "A GL_3 level analog of Selberg's result for S(t)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/anjb3epyt0t2c",
  "venue": "arXiv",
  "versions": []
}