{
  "abstract": "We study the $p$-adic valuation trees associated with the sequence \\[ e_n=\\int_0^\\infty e^{-t}F_n(t)\\,dt, \\] obtained by evaluating the Laplace transforms of the Fibonacci polynomials at $1$. We answer an open question of Givens and Moll in the negative by constructing an explicit counterexample showing that even internal branches need not be simple. We then reformulate the Givens--Moll lifting criteria for the even and odd subsequences in terms of the roots and derivatives of two associated polynomials. In particular, simple roots modulo $p$ give rise to simple internal branches. Finally, we develop a recursive lifting procedure that determines the unique surviving residue class at each level of a branch associated with a simple root and computes the $p$-adic valuations of the corresponding terms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37356",
  "author_total": 3,
  "authors": [
    {
      "name": "Rigoberto Flórez"
    },
    {
      "name": "Robinson Higuita-Diaz"
    },
    {
      "name": "José L. Ramírez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6kc9aje4gv1pn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37356",
  "fulltext_url": null,
  "id": "6kc9aje4gv1pn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37356",
  "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",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7224106684",
  "pdf_url": "https://arxiv.org/pdf/2610.37356",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6kc9aje4gv1pn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37356",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37356"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On $p$-Adic Valuation Trees Arising from Laplace Transform of Fibonacci Polynomials",
  "title_text": "On p-Adic Valuation Trees Arising from Laplace Transform of Fibonacci Polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/6kc9aje4gv1pn",
  "venue": "arXiv",
  "versions": []
}