{
  "abstract": "We prove zero density estimates for $L$-functions of cuspidal automorphic representations $π$ of $\\mathrm{GL}_2(\\mathbb{A}_{\\mathbb{Q}})$. We show that $N_π(σ, T) \\ll T^{\\frac{5}{2}(1 - σ) + o(1)}$, where $N_π(σ, T)$ denotes the number of zeros $ρ= β+ iγ$ of $L(s,π)$ with $β\\geq σ$ and $|γ| \\leq T$. The key input is an extension of the Guth$\\unicode{x2013}$Maynard argument to Dirichlet polynomials whose coefficients satisfy a weaker $\\ell^q$ bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27715",
  "author_total": 1,
  "authors": [
    {
      "name": "Catherine Cossaboom"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e0a3s4bwwc75c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27715",
  "fulltext_url": null,
  "id": "e0a3s4bwwc75c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27715",
  "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": "W7214226077",
  "pdf_url": "https://arxiv.org/pdf/2609.27715",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e0a3s4bwwc75c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27715",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27715"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Zero density estimates for $\\mathrm{GL}_2$ automorphic $L$-functions",
  "title_text": "Zero density estimates for GL_2 automorphic L-functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/e0a3s4bwwc75c",
  "venue": "arXiv",
  "versions": []
}