{
  "abstract": "We establish a regularized spectral decomposition of the squared magnitude of a maximal degenerate Eisenstein series as a Schwartz distribution on $\\mathrm{GL}_n$. Although the original problem is on $\\mathrm{GL}_n$, its spectral components are described entirely by the automorphic spectrum of $\\mathrm{GL}_2$. As an application, we prove a partial reciprocity formula relating the second moment of $\\mathrm{GL}_n\\times\\mathrm{GL}_n$ Rankin--Selberg central $L$-values and a mixed moment of $L$-values of $\\mathrm{GL}_2$. We also prove, assuming the generalized Ramanujan conjecture, an asymptotic formula for the second moment of the above Rankin--Selberg $L$-functions over a conductor-aspect family with an error term of square-root-cancellation strength.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01358",
  "author_total": 3,
  "authors": [
    {
      "name": "Jakub Dobrowolski"
    },
    {
      "name": "Subhajit Jana"
    },
    {
      "name": "Ramon Nunes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c2s7ry2qqa1hw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01358",
  "fulltext_url": null,
  "id": "c2s7ry2qqa1hw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01358",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7206180979",
  "pdf_url": "https://arxiv.org/pdf/2609.01358",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c2s7ry2qqa1hw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2609.01358",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01358"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Regularized spectral expansion of a Rankin--Selberg period and moments",
  "title_text": "Regularized spectral expansion of a Rankin--Selberg period and moments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/c2s7ry2qqa1hw",
  "venue": "arXiv",
  "versions": []
}