{
  "abstract": "Let $K$ be a hyperbolic knot and let $ρ_n$ be the $n$-dimensional irreducible representation induced from a lift of its holonomy representation. Motivated by Goda's asymptotic volume formula and the complexified Volume Conjecture, we study whether the higher-dimensional twisted Alexander invariants associated with $ρ_n$ detect the complex volume of the knot complement. We compute $$ \\fracπ{2} \\log \\left( \\frac{A_{K,n-2}(1)A_{K,n+2}(1)} {A_{K,n}(1)^2} \\right) $$ for all hyperbolic knots with at most six crossings. Our numerical experiments indicate that these values approach $$ \\operatorname{Vol}(S^3\\setminus K) +i\\,2π^2\\operatorname{CS}(S^3\\setminus K) $$ modulo $iπ^2\\mathbb{Z}$. Based on these computations, we propose a complexified analogue of Goda's asymptotic volume formula.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29124",
  "author_total": 1,
  "authors": [
    {
      "name": "Airi Aso"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1qy2xy95d21b2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29124",
  "fulltext_url": null,
  "id": "1qy2xy95d21b2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29124",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7214405720",
  "pdf_url": "https://arxiv.org/pdf/2609.29124",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1qy2xy95d21b2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29124",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29124"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Asymptotic behavior of twisted Alexander invariants for hyperbolic knots with at most six crossings",
  "title_text": "Asymptotic behavior of twisted Alexander invariants for hyperbolic knots with at most six crossings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/1qy2xy95d21b2",
  "venue": "arXiv",
  "versions": []
}