{
  "abstract": "For a polynomial of degree $n$ whose zeros lie in the closed unit disk, we determine the largest possible distance from a prescribed critical point of modulus $r$ to the nearest zero. If $n$ is even, the sharp radius is $\\sqrt{1-r^2}$; if $n$ is odd, the sharp radius is strictly smaller for $r\\in(0,1)$ and depends on $n$. Equality cases are also determined. The proof is based on the logarithmic-derivative identity and elementary geometric considerations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30284",
  "author_total": 2,
  "authors": [
    {
      "name": "Dragomir Grozev"
    },
    {
      "name": "Nikolai Nikolov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ab9se86wnes1a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30284",
  "fulltext_url": null,
  "id": "ab9se86wnes1a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30284",
  "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.CV"
    ],
    [
      "openalex",
      "2608|Analytic and geometric function theory"
    ]
  ],
  "openalex": "W7204920265",
  "pdf_url": "https://arxiv.org/pdf/2608.30284",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ab9se86wnes1a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30284",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30284"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Note on the Converse Sendov Problem",
  "title_text": "A Note on the Converse Sendov Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/ab9se86wnes1a",
  "venue": "arXiv",
  "versions": []
}