{
  "abstract": "At the critical density, the classical density theory of the Bargmann--Fock space no longer determines exact zero sets. We show that this failure is substantial: the complete radial counting function together with any prescribed finite collection of angular moments does not determine exact realizability, and the finite-dimensional relation between the dimension of the vanishing space and the zero-insertion capacity breaks down in infinite dimension. For arbitrary locally finite multisets, we establish a variational characterization of exact zero sets in terms of a renormalized logarithmic potential and relative entropy. This characterization yields sharp criteria for several classes of critical configurations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37704",
  "author_total": 2,
  "authors": [
    {
      "name": "Shengzhao Hou"
    },
    {
      "name": "Pan Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2qef91brwd6z0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37704",
  "fulltext_url": null,
  "id": "2qef91brwd6z0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37704",
  "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",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7214942637",
  "pdf_url": "https://arxiv.org/pdf/2609.37704",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2qef91brwd6z0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37704",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37704"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the zero sets of the Bargmann Fock space",
  "title_text": "On the zero sets of the Bargmann Fock space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/2qef91brwd6z0",
  "venue": "arXiv",
  "versions": []
}