{
  "abstract": "Using a deformed Borel-Laplace resummation, we propose a framework for repackaging quantum invariants as analytic invariants. We illustrate our approach through a detailed analysis of the coloured Jones polynomials of several simple knots, deriving explicit expressions for the resulting analytic invariants in terms of $(q,X)$-series. These invariants are closely related to, but generally distinct from, those obtained via the conventional Borel resummation of the Melvin-Morton-Rozansky expansion. As a further example, we construct an analytic invariant from a sequence of two-variable polynomials conjectured to be the Links-Gould polynomials of the figure-eight knot, associated with the quantum superalgebras $U_q(\\mathfrak{gl}(n|1))$. Finally, we apply our technique to $q$-series arising in the study of three-manifold invariants, revealing connections with mock modular forms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24247",
  "author_total": 3,
  "authors": [
    {
      "name": "Rinat Kashaev"
    },
    {
      "name": "Vladimir Mangazeev"
    },
    {
      "name": "Marcos Marino"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4say8cs99abvg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24247",
  "fulltext_url": null,
  "id": "4say8cs99abvg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24247",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
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      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.MP"
    ],
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      "arxiv",
      "math.QA"
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      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7223040809",
  "pdf_url": "https://arxiv.org/pdf/2610.24247",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4say8cs99abvg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.24247",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24247"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Analytic quantum invariants",
  "title_text": "Analytic quantum invariants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/4say8cs99abvg",
  "venue": "arXiv",
  "versions": []
}