{
  "abstract": "We prove a conjecture of Smyth on the Mahler measure of non-reciprocal trinomials of height $1$, determining exactly when their Mahler measures are greater than or less than $M(x+y+1)=ρ=1.381356\\ldots$, conjectured to be the smallest limit point of $M(P)$ for non-reciprocal polynomials. Conjecturally, our result gives the full spectrum of $M(P)<ρ$ for all non-reciprocal polynomials, not just for trinomials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37886",
  "author_total": 1,
  "authors": [
    {
      "name": "Paul M Voutier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7sec840pjpy7j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37886",
  "fulltext_url": null,
  "id": "7sec840pjpy7j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37886",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214966412",
  "pdf_url": "https://arxiv.org/pdf/2609.37886",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7sec840pjpy7j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37886",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37886"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Smyth's Conjecture on the Mahler Measure of non-reciprocal trinomials of height $1$",
  "title_text": "Smyth's Conjecture on the Mahler Measure of non-reciprocal trinomials of height $1$",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/7sec840pjpy7j",
  "venue": "arXiv",
  "versions": []
}