Year: 2026
Type: preprint
Abstract: Let $N$ be a sufficiently large real number. In this paper, it is proved that, for $10$, 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.
Source: arXiv (Cornell University)
Authors: Zhao, Yuhua, Li, Jinjiang, Long, Linji, Zhang, Min
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2900710960, G382562614, G55069091, G6461339978
OpenAlex ID: W7223252764