{
  "abstract": "Let \\(q=p^e\\) be a prime power and \\(n\\geq1\\). Let \\(L=\\F_{q^n}\\) and \\(K=\\F_q\\). We study the trace distribution of \\(r\\)-primitive \\(k\\)-normal elements of \\(L\\) over \\(K\\). We first derive exact formulas for the number of \\(k\\)-normal elements of \\(L\\) with a prescribed trace in \\(K\\). For \\(r\\mid q^n-1\\), \\(0\\leq k\\le n-1\\), and \\(a\\in K\\), let \\(\\mathcal{N}_{r,k}(a)\\) denote the number of \\(r\\)-primitive \\(k\\)-normal elements of \\(L\\) with trace \\(a\\). We establish a sufficient condition for \\(\\mathcal{N}_{r,k}\\) to be constant on \\(K^\\times\\). We also identify a subgroup \\(H_r\\) of \\(K^\\times\\) and prove that \\(\\mathcal{N}_{r,k}\\) is constant on each coset of \\(H_r\\). Finally, we obtain a necessary and sufficient character-sum condition for \\(\\mathcal{N}_{r,k}\\) to be constant on \\(K^\\times\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39510",
  "author_total": 2,
  "authors": [
    {
      "name": "Aakash Choudhary"
    },
    {
      "name": "Supriya Pisolkar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ngptx7na58as.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39510",
  "fulltext_url": null,
  "id": "4ngptx7na58as",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39510",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39510",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ngptx7na58as.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39510",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39510"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The trace distribution of $r$-primitive $k$-normal elements of finite fields",
  "title_text": "The trace distribution of r-primitive k-normal elements of finite fields",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/4ngptx7na58as",
  "venue": "arXiv",
  "versions": []
}