{
  "abstract": "We characterize all lattices $Λ\\subset \\mathbb{R}^2$ of rational density for which the Gabor system generated by the first Hermite function along $Λ$ is a frame for $L^2(\\mathbb{R})$. We prove that these are precisely the lattices whose density satisfies $D(Λ) = \\frac{q}{p} $ where $p,q \\in \\mathbb{N}$ are coprime with $q \\geq p+2$, thereby confirming a conjecture of Lyubarskii and Nes. A formalization of our main result in Lean $4$ is also included.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27846",
  "author_total": 3,
  "authors": [
    {
      "name": "Lukas Liehr"
    },
    {
      "name": "Irina Shafkulovska"
    },
    {
      "name": "Mitchell A. Taylor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0fnmassf6fy02.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27846",
  "fulltext_url": null,
  "id": "0fnmassf6fy02",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27846",
  "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"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7214184954",
  "pdf_url": "https://arxiv.org/pdf/2609.27846",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0fnmassf6fy02.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27846",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27846"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Derivatives of Theta Functions and a Problem of Lyubarskii and Nes",
  "title_text": "Derivatives of Theta Functions and a Problem of Lyubarskii and Nes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/0fnmassf6fy02",
  "venue": "arXiv",
  "versions": []
}