{
  "abstract": "We establish discorrelation estimates between the Piatetski-Shapiro prime set \\[ \\mathcal{P}_γ := \\{p \\text{ is prime and } p = \\lfloor n^{1/γ} \\rfloor \\text{ for some } n \\in \\mathbb{N}\\} \\] and arbitrary nilsequences when $γ\\in (0,1)$ is sufficiently close to $1$. This extends earlier works which treated linear or polynomial exponential phase functions. As an application, we establish an asymptotic formula for the number of solutions in $\\mathcal{P}_γ$ to any ``finite-complexity\" system of linear equations, including for the number of $k$-term arithmetic progressions in $\\mathcal{P}_γ$ up to a threshold $N$ for any given $k \\geq 3$. Furthermore, we show that there exists an absolute constant $C>0$ such that if \\[ 1 - 2^{-Ck} < γ< 1, \\] then the Piatetski-Shapiro primes $\\mathcal{P}_γ$ contain infinitely many non-trivial $k$-term arithmetic progressions. This significantly improves upon the previous range of $γ$ obtained by Li and Pan, which is of triple exponential type.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.18676",
  "author_total": 2,
  "authors": [
    {
      "name": "Xuancheng Shao"
    },
    {
      "name": "Yu-Chen Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4byam7xmw0nt9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.18676",
  "fulltext_url": null,
  "id": "4byam7xmw0nt9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.18676",
  "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.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7161729135",
  "pdf_url": "https://arxiv.org/pdf/2605.18676",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4byam7xmw0nt9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2605.18676",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.18676"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Linear equations in Piatetski-Shapiro primes",
  "title_text": "Linear equations in Piatetski-Shapiro primes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/4byam7xmw0nt9",
  "venue": "arXiv",
  "versions": []
}