{
  "abstract": "Let $F$ be a number field and $f$ a normalized cuspidal Hecke eigenform on $\\mathrm{GL}(2)$ over $F$, with $k/2$ as the central critical point of its $L$-function $L(f,s)$. Let $\\mathfrak{p}$ be a totally split prime ideal of $F$ lying above an odd prime $p$ and coprime to the level ideal of $f$. In this article, we show that $L(f\\otimesϕ, k/2)$ does not vanish for sufficiently ramified Hecke characters of $F$ of $p$-power order and $\\mathfrak{p}$-power conductor. Our result improves previous works of Jaesung Kwon and Hae-Sang Sun, in which the additional hypothesis that $p$ does not divide the class number of $F$ is required.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03976",
  "author_total": 1,
  "authors": [
    {
      "name": "Ruichen Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1wm4rnq3yv94b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03976",
  "fulltext_url": null,
  "id": "1wm4rnq3yv94b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03976",
  "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": "W7220673969",
  "pdf_url": "https://arxiv.org/pdf/2610.03976",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1wm4rnq3yv94b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.03976",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03976"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Nonvanishing of special $L$-values of cusp forms on $\\mathrm{GL}(2)$ with totally split prime power twists: without the class number hypothesis",
  "title_text": "Nonvanishing of special L-values of cusp forms on GL(2) with totally split prime power twists: without the class number hypothesis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/1wm4rnq3yv94b",
  "venue": "arXiv",
  "versions": []
}