{
  "abstract": "Let $D$ be an odd fundamental discriminant, with $D=1$ permitted, and let $r\\geq 1$ be fixed. We prove that, for every sufficiently large integer $\\ell$ satisfying $(-1)^\\ell D>0$, the first $r$ traced diagonal Rankin--Cohen brackets \\[ \\mathrm{Tr}_1^{|D|}[G_{\\ell-2e,D},G_{\\ell-2e,D}]_{2e}, \\qquad 1\\leq e\\leq r, \\] are linearly independent in $S_{2\\ell}(SL_2(\\mathbb Z))$. Here $G_{k,D}$ is the Eisenstein series of weight $k$, level $|D|$, and nebentypus $χ_D$. The Petersson formula of Kayath, Lane, Neifeld, Ni, and Xue then implies that at least $r$ normalized Hecke eigenforms $f\\in S_{2\\ell}(SL_2(\\mathbb Z))$ satisfy $L(f\\otimesχ_D,\\ell)\\neq 0$. For $D=1$, this gives, for every fixed $r$ and every sufficiently large $K\\equiv 0\\pmod 4$, at least $r$ level-one eigenforms of weight $K$ with nonzero central value.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19649",
  "author_total": 1,
  "authors": [
    {
      "name": "Ramin Takloo-Bighash"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c0xxzx3zky5qy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19649",
  "fulltext_url": null,
  "id": "c0xxzx3zky5qy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19649",
  "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",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7213589620",
  "pdf_url": "https://arxiv.org/pdf/2609.19649",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c0xxzx3zky5qy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19649",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19649"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Simultaneous nonvanishing of quadratic twists via Rankin-Cohen brackets",
  "title_text": "Simultaneous nonvanishing of quadratic twists via Rankin-Cohen brackets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/c0xxzx3zky5qy",
  "venue": "arXiv",
  "versions": []
}