论文标题
piatetski-shapiro prime二磷酸近似
Diophantine approximation by Piatetski-Shapiro primes
论文作者
论文摘要
令$ [\，\ cdot \，] $为地板功能。在本文中，我们表明，每当$η$真实时，常量$λ_i$满足了一些必要的条件，那么对于任何固定的$ 1 <c <38/37 $，存在无限的许多prime三元三分$ p_1，\，\，p_2，\，\，p_3 $满足inequality \ begin \ begin {equination {等式*equination {等式*equation*} |λ_1p_1p_1 +λ_1 +λ_1 +λ +λ +λ +λ +λ λ_3p_3+η| <（\ max p_j）^{{{\ frac {37c-38} {26c}}}}}（\ log \ log \ max p_j）^{10} {10} \ end {equation {equation {equation*}，因此
Let $[\,\cdot\,]$ be the floor function. In this paper we show that whenever $η$ is real, the constants $λ_i$ satisfy some necessary conditions, then for any fixed $1<c<38/37$ there exist infinitely many prime triples $p_1,\, p_2,\, p_3$ satisfying the inequality \begin{equation*} |λ_1p_1 + λ_2p_2 + λ_3p_3+η|<(\max p_j)^{{\frac{37c-38}{26c}}}(\log\max p_j)^{10} \end{equation*} and such that $p_i=[n_i^c]$, $i=1,\,2,\,3$.
