A Diophantine inequality with four prime variables

Min Zhang; Jinjiang Li

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arXiv · 1811.10397

A Diophantine inequality with four prime variables

Min Zhang·Jinjiang Li

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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.

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Min Zhang, Jinjiang Li. 2018-11-11. A Diophantine inequality with four prime variables. https://arxiv.org/abs/1811.10397

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