{
  "abstract": "Recently, Li obtained a mean Lindelöf estimate for the cubic moment of the central values of Maass form symmetric square $L$-functions over short intervals $(T-H, T+H)$ of length $H \\ge T^{18/19+ε}$. We improve this result by showing that the estimate holds for $H \\gg T^{6/7+ε}$. The key ingredient in our proof is a new asymptotic formula for the second twisted moment of Maass symmetric square $L$-functions. Based on this formula, we also improve the lower bound for the proportion of non-vanishing central $L$-values in short intervals. Previously, even under the assumption of the Lindelöf hypothesis for Dirichlet $L$-functions, the proportion of non-vanishing values in intervals of length $H = T^β$ was only known to be at least $\\frac{3β-1}{4}$. We establish an unconditional lower bound of $\\frac{7β-2}{8}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11119",
  "author_total": 2,
  "authors": [
    {
      "name": "Olga Balkanova"
    },
    {
      "name": "Dmitry Frolenkov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7fjw5pn6sy5wy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11119",
  "fulltext_url": null,
  "id": "7fjw5pn6sy5wy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11119",
  "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/2609.11119",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7fjw5pn6sy5wy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11119",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11119"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Moments and Non-Vanishing of Maass Form Symmetric Square L-Functions in Short Intervals",
  "title_text": "Moments and Non-Vanishing of Maass Form Symmetric Square L-Functions in Short Intervals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/7fjw5pn6sy5wy",
  "venue": "arXiv",
  "versions": []
}