{
  "abstract": "We study iterates of a quadratic $f= x^2+1/c\\in K[x]$. If the number of factors of $f^n:=f\\circ f \\circ ... \\circ f$ is bounded by a constant independent of $n$, then $f$ is said to be \\emph{eventually stable}. This paper is an extension to $\\mathbb{Q}(i)$ of the paper \\cite{evstb}, which considered $f$ over $\\mathbb{Q}$. The conjecture \"if $f^2$ is irreducible, then $f^n$ is irreducible for all $n$\" extends to $\\mathbb{Q}(i)$, but due to the lack of a linear ordering on $\\mathbb{Q}(i)$, an auxiliary function is involved in a specific $n$ to check. The elusive case of $c\\equiv 2 \\bmod 4$ (as a $\\mathbb{Z}$ equivalence class) is shown to be \"stable\" over $\\mathbb{Q}(i)$, offering more evidence for \\cite[Conjecture 1]{evstb}. Stability for $c\\equiv 1\\bmod 2$ (as a $\\mathbb{Z}[i]$ equivalence class) is not as fully handled as over $\\mathbb{Z}$, however.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.25250",
  "author_total": 1,
  "authors": [
    {
      "name": "Jermain McDermott"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6772pa87pajmh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.25250",
  "fulltext_url": null,
  "id": "6772pa87pajmh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.25250",
  "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.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7165938401",
  "pdf_url": "https://arxiv.org/pdf/2606.25250",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6772pa87pajmh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2606.25250",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.25250"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Stable quadratic polynomials over $\\mathbb{Q}(i)$",
  "title_text": "Stable quadratic polynomials over ℚ(i)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/6772pa87pajmh",
  "venue": "arXiv",
  "versions": []
}