标题： 关于 Piatetski-Shapiro 素数上$αp$模一的分布 显示英文标题

标题： On the distribution of $αp$ modulo one over Piatetski-Shapiro primes

摘要： 设$[\, \cdot\,]$为取整函数，$\|x\|$表示$x$到最近整数的距离。 在本文中，我们证明了当$\alpha$为无理数且$\beta$为实数时，对于任何固定的$1<c<12/11$，存在无限多个满足不等式\begin{equation*} \|\alpha p+\beta\|\ll p^{\frac{11c-12}{26c}}\log^6p \end{equation*}的素数$p$，并且满足$p=[n^c]$。 显示英文摘要

摘要： Let $[\, \cdot\,]$ be the floor function and $\|x\|$ denotes the distance from $x$ to the nearest integer. In this paper we show that whenever $\alpha$ is irrational and $\beta$ is real then for any fixed $1<c<12/11$ there exist infinitely many prime numbers $p$ satisfying the inequality \begin{equation*} \|\alpha p+\beta\|\ll p^{\frac{11c-12}{26c}}\log^6p \end{equation*} and such that $p=[n^c]$.