{
  "abstract": "Using Soundararajan's resonance method, we obtain extreme values of the central derivatives \\[ L^{(r)}(1/2,f\\otimesχ_d), \\] where $f$ is a normalized newform and $χ_d$ ranges over primitive real characters associated with negative fundamental discriminants. The twisted first moment estimate used in the proof may be of independent interest. Applying Gross--Zagier-type formulas, we obtain correspondingly large Néron--Tate heights of Heegner points on elliptic curves and large absolute values of Beilinson--Bloch heights of Heegner cycles attached to modular forms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26786",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohammad H. Hamdar"
    },
    {
      "name": "Sun-Kai Leung"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/26yt54cwrd9c2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26786",
  "fulltext_url": null,
  "id": "26yt54cwrd9c2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26786",
  "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",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214097245",
  "pdf_url": "https://arxiv.org/pdf/2609.26786",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/26yt54cwrd9c2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26786",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26786"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Extreme values of central $L$-derivatives and heights of Heegner points",
  "title_text": "Extreme values of central L-derivatives and heights of Heegner points",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/26yt54cwrd9c2",
  "venue": "arXiv",
  "versions": []
}