{
  "abstract": "We introduce $L$-functions associated with characters of the Jacobian of a finite graph, as a graph-theoretic analogue of the $L$-functions arising from unramified coverings of algebraic curves. These $L$-functions are defined using the Riemann--Roch structure on the graph and extend Lorenzini's two-variable zeta function. We show that if two connected graphs without bridges have isomorphic Jacobians and their $L$-functions agree under the induced correspondence of characters, then their Laplacian lattices coincide. We also show that these $L$-functions satisfy a functional equation. Finally, we give examples showing that neither the Jacobian nor the Lorenzini zeta function alone determines the Laplacian lattice.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29981",
  "author_total": 2,
  "authors": [
    {
      "name": "Daniel Labib"
    },
    {
      "name": "Antonio Lei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c27m4g27n76ra.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29981",
  "fulltext_url": null,
  "id": "c27m4g27n76ra",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29981",
  "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.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7204891556",
  "pdf_url": "https://arxiv.org/pdf/2608.29981",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c27m4g27n76ra.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2608.29981",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29981"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Recovering Laplacian Lattices from $L$-Functions of Graphs",
  "title_text": "Recovering Laplacian Lattices from L-Functions of Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/c27m4g27n76ra",
  "venue": "arXiv",
  "versions": []
}