{
  "abstract": "Let $f$ and $g$ be Hecke--Maass cusp forms of $\\operatorname{SL}_2(\\mathbb{Z})$, with spectral parameters $t_f$ and $t_g$, respectively. Let $T$ be a large parameter and put $L = |T-t_g|.$ We prove the Lindelöf-on-average estimate \\[ \\sum_{ |t_f-T|\\leq H} \\left|L\\!\\left(\\frac12,f\\otimes g\\right)\\right|^2 \\ll_{\\varepsilon} T^{1+\\varepsilon}H, \\] uniformly in the range \\[ T^{1/3+\\varepsilon}\\ll H,\\qquad HT^\\varepsilon\\ll L\\leq T. \\] As an immediate consequence, in the generic range when both $|t_g|$ and $L$ are of size $T$, we obtain the Weyl bound \\[ L\\!\\left(\\frac12,f\\otimes g\\right) \\ll_\\varepsilon C(f\\times g)^{1/6+\\varepsilon}. \\]",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27804",
  "author_total": 1,
  "authors": [
    {
      "name": "Zihao Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0d4wjaf6fz332.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27804",
  "fulltext_url": null,
  "id": "0d4wjaf6fz332",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27804",
  "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": "W7223122232",
  "pdf_url": "https://arxiv.org/pdf/2610.27804",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0d4wjaf6fz332.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27804",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27804"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Weyl Bounds for $\\operatorname{GL}_2\\times \\operatorname{GL}_2$ Rankin--Selberg $L$-functions via Short Spectral Moments",
  "title_text": "Weyl Bounds for GL_2× GL_2 Rankin--Selberg L-functions via Short Spectral Moments",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/0d4wjaf6fz332",
  "venue": "arXiv",
  "versions": []
}