{
  "abstract": "We consider a real even Hecke-Maass cusp form $ϕ$ on the modular surface, with Laplace eigenvalue $1/4+T^2$. We prove that its restriction to any fixed compact segment $β$ of the vertical geodesic above $i$ has $\\gg_{β,\\varepsilon} T^{1/6-\\varepsilon}$ sign changes, yielding the same lower bound for the number of distinct inert nodal domains meeting the segment. Building on ideas of Jang-Jung and Jung-Young, we study correlations between values at points on the vertical geodesic separated by distances of order $T^{-1}$. Using arithmetic quantum unique ergodicity and Dirichlet-polynomial estimates, we show that the correlation is negative for a suitable choice of separation. An elementary counting argument and the Iwaniec-Sarnak supremum bound then give the claimed lower bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31857",
  "author_total": 1,
  "authors": [
    {
      "name": "Peter Zenz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/46f636vewas8q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31857",
  "fulltext_url": null,
  "id": "46f636vewas8q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31857",
  "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.NT"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7223689611",
  "pdf_url": "https://arxiv.org/pdf/2610.31857",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/46f636vewas8q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.31857",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31857"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quantitative nodal domain count for Maass forms",
  "title_text": "Quantitative nodal domain count for Maass forms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/46f636vewas8q",
  "venue": "arXiv",
  "versions": []
}