{
  "abstract": "Let $c>1$ be noninteger, and let $Λ$ denote the von Mangoldt function. The averages \\[ A_N^{c} f(x):=\\frac1N\\sum_{n=1}^{N} Λ(n)f\\bigl(T^{\\lfloor n^c\\rfloor}x\\bigr) \\] satisfy the variational estimate \\[ \\bigl\\|\\mathcal{V}^r(A_N^{c} f:N\\in\\mathbb{N})\\bigr\\|_{L^p(X)} \\lesssim_{c,p,r}\\|f\\|_{L^p(X)} \\] for every $1<p<\\infty$ and $r>2$, on every $σ$-finite measure-preserving system. In particular, the normalized averages along fractional powers of primes converge almost everywhere. The main arithmetic ingredient is a uniform bound on the correlations of $Λ-1$ with fractional-power exponential phases, yielding arbitrarily large powers of logarithmic gain. We obtain this estimate through short-interval polynomial approximation of the fractional phase and higher-order discorrelation estimates. The same approach yields almost-everywhere convergence to for the Möbius-weighted averages along $\\left( \\lfloor n^c \\rfloor \\right)_{n \\in \\mathbb{N}}$ throughout $1<p<\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02465",
  "author_total": 1,
  "authors": [
    {
      "name": "Anastasios Fragkos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c6szq8wvaf9ne.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02465",
  "fulltext_url": null,
  "id": "c6szq8wvaf9ne",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02465",
  "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.CA"
    ],
    [
      "arxiv",
      "math.DS"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02465",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c6szq8wvaf9ne.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02465",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02465"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Pointwise Ergodic Theorems Along $\\lfloor p^c\\rfloor$ for Every $c>1$",
  "title_text": "Pointwise Ergodic Theorems Along ⌊ p^c⌋ for Every c>1",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/c6szq8wvaf9ne",
  "venue": "arXiv",
  "versions": []
}