论文标题
$ \ mathbf {p = x^2+y^2+1} $的Quaternary piatetski-shapiro不平等
The quaternary Piatetski-Shapiro inequality with one prime of the form $\mathbf{p=x^2+y^2+1}$
论文作者
论文摘要
在本文中，我们表明，对于任何固定的$ 1 <c <967/805 $，每个足够大的正数$ n $和一个小的常数$ \ varepsilon> 0 $，diophantine不平等\ begin {equation*} | p_1 | p_1^c+p_2^c+p_2^c+p_3^c+p_3^c+p_4^c+p_4^c+p_4^c n | < $ p_1，\，p_2，\，p_3，\，p_4 $，以便$ p_1 = x^2 + y^2 + 1 $。
In this paper we show that, for any fixed $1<c<967/805$, every sufficiently large positive number $N$ and a small constant $\varepsilon>0$, the diophantine inequality \begin{equation*} |p_1^c+p_2^c+p_3^c+p_4^c-N|<\varepsilon \end{equation*} has a solution in prime numbers $p_1,\,p_2,\,p_3,\,p_4$, such that $p_1=x^2 + y^2 +1$.
