{
  "abstract": "This work analyzes the spectral zeta function associated with regular and singular Sturm--Liouville operators endowed with $N$ generalized point potentials. The point interactions are characterized as a particular class of self-adjoint extensions of Sturm--Liouville operators defined on a chain of $N+1$ adjacent intervals. Each interaction is described by $SL(2,\\R)$ matching conditions relating generalized boundary values across neighboring intervals. We construct the spectral zeta function associated with Sturm--Liouville operators endowed with $N$ generalized point potentials in terms of a contour integral involving an appropriate characteristic function. The process of analytic continuation of the spectral zeta function to a neighborhood of the origin is illustrated by means of specific examples where the $ζ$-regularized functional determinant is also explicitly computed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19322",
  "author_total": 2,
  "authors": [
    {
      "name": "Guglielmo Fucci"
    },
    {
      "name": "Jonathan Stanfill"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/35q1x6pmmb129.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19322",
  "fulltext_url": null,
  "id": "35q1x6pmmb129",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19322",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7213585956",
  "pdf_url": "https://arxiv.org/pdf/2609.19322",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/35q1x6pmmb129.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.19322",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19322"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "The spectral $ζ$-function of Sturm--Liouville operators with $N$ generalized point potentials",
  "title_text": "The spectral ζ-function of Sturm--Liouville operators with N generalized point potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/35q1x6pmmb129",
  "venue": "arXiv",
  "versions": []
}