{
  "abstract": "Assuming the Riemann Hypothesis, Montgomery established results concerning pair correlation of zeros of the Riemann zeta function. Rudnick and Sarnak extended these results to automorphic $L$-functions and all level correlations. We discover additional geometric structures associated to the zeros of automorphic $L$-functions. In the case of pair correlation, these structures form certain surfaces which display Gaussian behavior. For triple correlation, these structures exhibit Laplace and Chi-squared distributions, revealing an unexpected phase transition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26575",
  "author_total": 3,
  "authors": [
    {
      "name": "Debmalya Basak"
    },
    {
      "name": "Cruz Castillo"
    },
    {
      "name": "Alexandru Zaharescu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4phknsdw1mjqc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26575",
  "fulltext_url": null,
  "id": "4phknsdw1mjqc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26575",
  "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"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7223010804",
  "pdf_url": "https://arxiv.org/pdf/2610.26575",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4phknsdw1mjqc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26575",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26575"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Surfaces Associated to Zeros of Automorphic $L$-functions",
  "title_text": "Surfaces Associated to Zeros of Automorphic L-functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/4phknsdw1mjqc",
  "venue": "arXiv",
  "versions": []
}