{
  "abstract": "A number field $K$ is called \\emph{monogenic} if its ring of integers $\\mathbb{Z}_K$ can be expressed as a simple ring extension $\\mathbb{Z}[α]$ for some $α\\in \\mathbb{Z}_K$. A monic irreducible polynomial $f(x)\\in\\mathbb{Z}[x]$ is said to be monogenic if one of its roots generates both the number field and its ring of integers. In this article, we establish the necessary and sufficient conditions for $[\\mathbb{Z}_{K_i}:\\mathbb{Z}[α_i]]=1$, where $K_i=\\mathbb{Q}(α_i)$ and $α_i$ is a root of the composed polynomial $f_i(x^k+b)$ for $i=1,2$. Here, $f_1(x)=x^n+c\\sum_{j=1}^{n}(ax)^{n-j}\\in\\mathbb{Z}[x]$ and $f_2(x)=x^n+c\\sum_{j=1}^{n}a^{j-1}x^{n-j}\\in\\mathbb{Z}[x]$ are irreducible polynomials of degree $n\\ge 3$. In addition, we derive asymptotic estimates for the number of monogenic polynomials in these families under natural assumptions. As an application of our main results, we construct a class of polynomials with non-square-free discriminants. We also analyze the behavior of solutions to certain related differential equations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.00949",
  "author_total": 3,
  "authors": [
    {
      "name": "Anuj Jakhar"
    },
    {
      "name": "Ravi Kalwaniya"
    },
    {
      "name": "Prabhakar Yadav"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0wej85chn5bcj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.00949",
  "fulltext_url": null,
  "id": "0wej85chn5bcj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.00949",
  "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",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7160304952",
  "pdf_url": "https://arxiv.org/pdf/2605.00949",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0wej85chn5bcj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2605.00949",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.00949"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Monogenic Fields from Polynomial Compositions with Applications",
  "title_text": "Monogenic Fields from Polynomial Compositions with Applications",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/0wej85chn5bcj",
  "venue": "arXiv",
  "versions": []
}