{
  "abstract": "Let $p$ be an odd prime, and let $a_n$ be the reduction modulo $p$ of the $n$th coefficient of the Artin-Hasse exponential. We study the weighted $p$-section convolutions $W_k$ formed from the coefficients $a_{kp}$. We prove the conjecture of Avitabile and Mattarei for $1<k<p$ and extend it to a single global power-series identity determining the entire sequence $(W_k)_{k\\geq 0}$. This identity yields an explicit base-$p$ digit formula; in particular, $(W_k)$ is $p$-automatic and admits an explicit finite-state evaluator. Independently, the exact conjugated $p$-section equation gives a strict $p$-adic fixed-point iteration for the logarithmic derivative of the $p$-section. Big-Witt reconstruction then recovers the $p$-section, and hence all coefficients of the Artin-Hasse exponential, to arbitrary prescribed $p$-adic precision by a purely modular procedure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07761",
  "author_total": 1,
  "authors": [
    {
      "name": "Ben Clare"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/628wtzb1tvka7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07761",
  "fulltext_url": null,
  "id": "628wtzb1tvka7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07761",
  "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",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7212075000",
  "pdf_url": "https://arxiv.org/pdf/2609.07761",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/628wtzb1tvka7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07761",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07761"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Artin-Hasse $p$-section: weighted convolutions and $p$-adic recovery",
  "title_text": "The Artin-Hasse p-section: weighted convolutions and p-adic recovery",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/628wtzb1tvka7",
  "venue": "arXiv",
  "versions": []
}