{
  "abstract": "In this paper, we address the subconvexity problem in level aspect for symmetric square $L$-functions for cuspidal automorphic representation of $\\mathrm{GL}_2(\\mathbb{Q})$ with a prescribed local ramification at prime $p$. To be more precise, let $π$ be a tempered cuspidal automorphic representation of conductor $q(π)=p^2$ with a non-quadratic central character of conductor $p$. We prove that if the corresponding local representation $π_p$ belongs to a suitable class of representations $\\mathcal S$, then \\[ L\\left(\\frac{1}{2},\\,\\mathrm{Sym}^2π\\right)\\ll_{\\varepsilon, π_\\infty} q(\\mathrm{Sym}^2π)^{\\frac{1}{4}-\\frac{1}{168}+o(1)}, \\] where implied constant depends polynomially on the spectral parameters of $π_\\infty$. This is the first instance of level-aspect subconvex bound for $L$-functions of a $\\mathrm{GL}_3(\\mathbb Q)$ automorphic representation. Our approach is based on the delta-symbol method. Apart from some standard analytic number theoretic tools, Katz's theory of hypergeometric sums, and Deligne's proof of Weil-conjectures play an important role in the proof.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04155",
  "author_total": 1,
  "authors": [
    {
      "name": "Pratim Mitra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e7qtnf9r731ps.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04155",
  "fulltext_url": null,
  "id": "e7qtnf9r731ps",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04155",
  "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",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7208705756",
  "pdf_url": "https://arxiv.org/pdf/2609.04155",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e7qtnf9r731ps.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.04155",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04155"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The subconvexity problem for symmetric square $L$-functions in level aspect",
  "title_text": "The subconvexity problem for symmetric square L-functions in level aspect",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/e7qtnf9r731ps",
  "venue": "arXiv",
  "versions": []
}