{
  "abstract": "We begin the study of the beyond endoscopic trace formula for $\\mathrm{GL}_2$ over $\\mathbb{Q}$ attached to any symmetric power representation $σ_k$ of the dual group $\\mathrm{G}L_2(\\mathbb{C})$. For an adelic function that incorporates the $L$-functions $L(s_B,π,σ_k)$ through the basic functions at all the finite places, we integrate the cuspidal kernel against a corresponding Eisenstein series $E(g,s)$ and realize the trace formula as a residue at $s=1$, replacing Arthur's truncation operation by a continuously deformed trace formula. We argue Poisson summation on the trace variable of the Hitchin-Steinberg base and show that the dominant term of the elliptic part admits meromorphic continuation to $\\mathfrak{R}(s_B) \\geq 0$ with a pole of order $k$ at $s_B =1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01990",
  "author_total": 1,
  "authors": [
    {
      "name": "Pranjal Pandurang Warade"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1zrgz2jp1enj7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01990",
  "fulltext_url": null,
  "id": "1zrgz2jp1enj7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01990",
  "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",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7207713522",
  "pdf_url": "https://arxiv.org/pdf/2609.01990",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1zrgz2jp1enj7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.01990",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01990"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Jacquet-Zagier treatment of the beyond endoscopy trace formula for $\\mathrm{GL}_2$",
  "title_text": "Jacquet-Zagier treatment of the beyond endoscopy trace formula for GL_2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/1zrgz2jp1enj7",
  "venue": "arXiv",
  "versions": []
}