{
  "abstract": "We study the roots and the Mahler measure of the $Q$-polynomial of links. We first consider links obtained by adding twists to a pair of parallel strands. We prove that the Mahler measure of the transformed $Q$-polynomial converges as the number of twists increases. We also show that all but a uniformly bounded number of distinct roots of the $Q$-polynomial approach the real interval $[-2,2]$. This behavior is different from that of the roots of the Jones polynomial under twisting. Numerical experiments on prime knots lead us to a conjecture about the roots of the transformed $Q$-polynomial of alternating knots. Finally, we compare real and unit-circle roots of the Alexander, Jones, and $Q$-polynomials, and give an infinite family of $2$-bridge links whose $Q$-polynomials have only real nonzero roots.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05200",
  "author_total": 1,
  "authors": [
    {
      "name": "Kotaro Shoji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/atqm4ekwjfqcn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05200",
  "fulltext_url": null,
  "id": "atqm4ekwjfqcn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05200",
  "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"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7211887406",
  "pdf_url": "https://arxiv.org/pdf/2609.05200",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/atqm4ekwjfqcn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.05200",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05200"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the Mahler measure and root distribution of the $Q$-polynomial of links",
  "title_text": "On the Mahler measure and root distribution of the Q-polynomial of links",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/atqm4ekwjfqcn",
  "venue": "arXiv",
  "versions": []
}