A Diophantine inequality with four prime variables

Min Zhang; Jinjiang Li

A Diophantine inequality with four prime variables

Number Theory 2018-11-27 v1

Authors: Min Zhang , Jinjiang Li

Abstract

Let $N$ be a sufficiently large real number. In this paper, it is proved that, for $1<c<\frac{1193}{889}$ , the following Diophantine inequality \begin{equation*} \big|p_1^c+p_2^c+p_3^c+p_4^c-N\big|<\log^{-1}N \end{equation*} is solvable in prime variables $p_1,p_2,p_3,p_4$ , which improves the result of Mu.

Keywords

diophantine equations

Cite

@article{arxiv.1811.10397,
  title  = {A Diophantine inequality with four prime variables},
  author = {Min Zhang and Jinjiang Li},
  journal= {arXiv preprint arXiv:1811.10397},
  year   = {2018}
}

Comments

13 pages. arXiv admin note: substantial text overlap with arXiv:1810.09368

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