{
  "abstract": "For $1\\le p < \\infty$, $φ_p$ is the function of minimal $L^p$ norm among all functions $f$ of exponential type at most $π$ for which $f(0)=1$. We start from the ansatz that the positive zeros $τ_n$ of $φ_p$ are close to \\(n+1/p-1/2\\) and use a weighted convex correction to first place them in an \\(\\ell^2\\)-neighborhood of this sequence. A bootstrap argument then improves this to a {Poincaré asymptotic} expansion of $τ_n-(n+\\frac1p-\\frac12)$ in terms of odd powers of $(n+\\frac1p-\\frac12)^{-1}$. We also get precise information about the Fourier transform $\\widehatφ_p$, a result that in particular implies that for all integers $n\\ge 2$, $\\widehatφ_{2n}$ is an integrable function which, when convolved with itself $2n-2$ times, is constant on the interval $[-π,π]$. In particular, we identify the extremizer in an autoconvolution problem posed by B. Green in 2001.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19132",
  "author_total": 3,
  "authors": [
    {
      "name": "Andriy Bondarenko"
    },
    {
      "name": "Joaquim Ortega-Cerdà"
    },
    {
      "name": "Kristian Seip"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dyc3xg8y2c0tc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19132",
  "fulltext_url": null,
  "id": "dyc3xg8y2c0tc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19132",
  "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.CA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7222332939",
  "pdf_url": "https://arxiv.org/pdf/2610.19132",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dyc3xg8y2c0tc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19132",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19132"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The zeros of point evaluation extremals in Paley-Wiener spaces",
  "title_text": "The zeros of point evaluation extremals in Paley-Wiener spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/dyc3xg8y2c0tc",
  "venue": "arXiv",
  "versions": []
}