论文标题
由$ \ mathbf {p = x^2+y^2+1} $的一种形式之一的素质的三元性不平等
A ternary diophantine inequality by primes with one of the form $\mathbf{p=x^2+y^2+1}$
论文作者
论文摘要
在本文中，我们解决了特殊形式的质量数量的三元piatetski-shapiro不平等。更准确地说，我们表明，对于任何固定的$ 1 <c <\ frac {427} {400} $，每个足够大的正数$ n $和一个小常数$ \ varepsilon> 0 $，diophantine norquality \ begin \ begin {equination {equination*} | p_1^c+p_1^c+p_2^c+p_2^c+p_3^c n}具有质数中的解决方案$ p_1，\，p_2，\，p_3 $，因此$ p_1 = x^2 + y^2 + 1 $。为此，我们建立了一个新的Bombieri -Vinogradov类型的结果，以实现素数的指数款项。
In this paper we solve the ternary Piatetski-Shapiro inequality with prime numbers of a special form. More precisely we show that, for any fixed $1<c<\frac{427}{400}$, 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-N|<\varepsilon \end{equation*} has a solution in prime numbers $p_1,\,p_2,\,p_3$, such that $p_1=x^2 + y^2 +1$. For this purpose we establish a new Bombieri -- Vinogradov type result for exponential sums over primes.
