{
  "abstract": "Let $N$ be a sufficiently large real number. In this paper, it is proved that, for $1<c<\\frac{5179}{3909}$ and for any arbitrary large number $E>0$, the Diophantine inequality \\begin{equation*} \\big|p_1^c+p_2^c+p_3^c+p_4^c-N\\big|<(\\log N)^{-E} \\end{equation*} is solvable in prime variables $p_1,p_2,p_3,p_4$ such that each of the numbers $p_i+2\\,(i=1,2,3,4)$ has, counted according to multiplicity, at most $[\\frac{31250}{5179-3909c}]$ prime factors, which constitutes a large improvement upon the previous results of Dimitrov [13] and Li-Xue-Zhang [22], respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28774",
  "author_total": 4,
  "authors": [
    {
      "name": "Yuhua Zhao"
    },
    {
      "name": "Jinjiang Li"
    },
    {
      "name": "Linji Long"
    },
    {
      "name": "Min Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2gdgs562v0jhn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28774",
  "fulltext_url": null,
  "id": "2gdgs562v0jhn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28774",
  "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": "W7223252764",
  "pdf_url": "https://arxiv.org/pdf/2610.28774",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2gdgs562v0jhn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.28774",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28774"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A quaternary Diophantine inequality with prime numbers of a special form (II)",
  "title_text": "A quaternary Diophantine inequality with prime numbers of a special form (II)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/2gdgs562v0jhn",
  "venue": "arXiv",
  "versions": []
}