{
  "abstract": "We prove the Edholm--Mathew nonvanishing conjecture for the palindromic polynomials associated with rational Hartogs triangles. For relatively prime positive integers $m>n$, we show that $e^{-i(m-n)θ}Q_{m,n}(e^{iθ})$ is strictly positive for every real $θ$ and derive an explicit lower bound. The proof expresses this trigonometric polynomial as a finite average of products of unnormalized Fejér kernels. It follows that $Q_{m,n}$ has exactly $m-n$ zeros in the punctured unit disc, counted with multiplicity. As a consequence, a rational Hartogs triangle has a zero-free Bergman kernel if and only if its exponent is the reciprocal of a positive integer.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07480",
  "author_total": 2,
  "authors": [
    {
      "name": "Guantie Deng"
    },
    {
      "name": "Qian Fu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/06bqfvkr3b20t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07480",
  "fulltext_url": null,
  "id": "06bqfvkr3b20t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07480",
  "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.CV"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07480",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/06bqfvkr3b20t.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07480",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07480"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Bergman Kernel Zeros on Rational Hartogs Triangles",
  "title_text": "Bergman Kernel Zeros on Rational Hartogs Triangles",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/06bqfvkr3b20t",
  "venue": "arXiv",
  "versions": []
}