{
  "abstract": "Let N be a sufficiently large odd integer. We study the representation of a large integer m N^k as a sum of m almost equal k-th powers of primes, where the common distribution scale is at least N^theta. Assuming the Generalized Riemann Hypothesis (GRH), we prove that for any epsilon > 0 one may take theta > 1/2, provided that m < k(k+1)/2 and that m, k are odd integers sufficiently large. This is achieved by employing a new tool closely related to earlier work. For sufficiently large m, by refining the discussion of the minor arcs, we further show that under GRH the equation has a solution provided m > 16k log k + 4k + 2. Moreover, we give an asymptotic formula for the number of solutions, with main term involving N^{2k theta (1 - (1 - 1/k)^{m_1}) + theta(m-1) + 1 - k}, where m_1 = 4k. Under GRH and for sufficiently large m, k, the short-interval Waring-Goldbach problem is essentially settled.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16048",
  "author_total": 1,
  "authors": [
    {
      "name": "YaoJie Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/97axrts71er8z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16048",
  "fulltext_url": null,
  "id": "97axrts71er8z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16048",
  "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|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7213410634",
  "pdf_url": "https://arxiv.org/pdf/2609.16048",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/97axrts71er8z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16048",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16048"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Waring-Goldbach problem in short intervals under the Generalized Riemann Hypothesis",
  "title_text": "The Waring-Goldbach problem in short intervals under the Generalized Riemann Hypothesis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/97axrts71er8z",
  "venue": "arXiv",
  "versions": []
}