{
  "abstract": "Let $u_j $ traverse an orthonormal basis of Hecke--Maass forms for $\\mathrm{SL}_2 (\\mathbb {Z}) $ with Hecke eigenvalues $λ_j (n)$ and Laplace eigenvalue $1/4+t_j^2$. In this paper, we consider the short-interval variant of the twisted spectral large sieve inequality of Luo for $ λ_j (n) n^{it_j} $ on the range $t_j \\leqslant T$ and prove that the `Eisenstein--Kloosterman' cancellation discovered by Luo is effective on the interval $ T < t_j \\leqslant T + M $ as long as $\\sqrt{T} < M \\leqslant T$. Moreover, our approach yields an improvement of the large sieve inequality of Luo.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29558",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhi Qi"
    },
    {
      "name": "Ruihua Qiao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1m8es5tzjzezn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29558",
  "fulltext_url": null,
  "id": "1m8es5tzjzezn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29558",
  "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": "W7204896888",
  "pdf_url": "https://arxiv.org/pdf/2608.29558",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1m8es5tzjzezn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2608.29558",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29558"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Luo's Spectral Large Sieve Inequality on Short Intervals",
  "title_text": "Luo's Spectral Large Sieve Inequality on Short Intervals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/1m8es5tzjzezn",
  "venue": "arXiv",
  "versions": []
}