{
  "abstract": "Let $R=GR(p^m,p^{mf})$, where $p$ is prime, $q=p^f$, $m,f\\geq1$, $d\\geq2$ and $p\\nmid d$. We count $n$-element subsets of $P=\\{x^d:x\\in R\\}\\setminus\\{0\\}$, the set of distinct nonzero $d$th-power values, with a prescribed sum. For fixed $m,d,n$ with $n\\geq3$, the count equals \\[ q^{-m}\\binom{|P|}{n}(1+O_{m,d,n}(q^{1-n/2})) \\] as $q\\to\\infty$ through admissible prime powers, uniformly over all targets and with both $p$ and $f$ allowed to vary. For fixed $m,d$, we also classify uniform relative equidistribution at the remaining positive sizes: it fails at $n=1$, and at $n=2$ it holds along an admissible sequence if and only if, for all sufficiently large terms, $\\gcd(d,q-1)=1$ and $(m\\geq2\\text{ or }p\\ne2)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28837",
  "author_total": 1,
  "authors": [
    {
      "name": "Zijie Gu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3w1drmbntd6y9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28837",
  "fulltext_url": null,
  "id": "3w1drmbntd6y9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28837",
  "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|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7223222127",
  "pdf_url": "https://arxiv.org/pdf/2610.28837",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3w1drmbntd6y9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.28837",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28837"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Subset sums of power values over Galois rings",
  "title_text": "Subset sums of power values over Galois rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/3w1drmbntd6y9",
  "venue": "arXiv",
  "versions": []
}