论文标题
关于$αp$ modulo在piatetski-shapiro prime上的分布
On the distribution of $αp$ modulo one over Piatetski-Shapiro primes
论文作者
论文摘要
令$ [\，\ cdot \，] $为落地功能，$ \ | x \ | $表示从$ x $到最近整数的距离。在本文中，我们表明，每当$α$都是不合理的并且$β$是真实的，那么对于任何固定的$ 1 <c <12/11 $，都存在无限的许多质量数字$ p $满足不等式的\ begin {equation*} \ | | | |αp+β\ | \ | \ | \ | \ ll p^{\ frac {\ frac {\ frac { \ end {equation*}，使得$ p = [n^c] $。
Let $[\, \cdot\,]$ be the floor function and $\|x\|$ denotes the distance from $x$ to the nearest integer. In this paper we show that whenever $α$ is irrational and $β$ is real then for any fixed $1<c<12/11$ there exist infinitely many prime numbers $p$ satisfying the inequality \begin{equation*} \|αp+β\|\ll p^{\frac{11c-12}{26c}}\log^6p \end{equation*} and such that $p=[n^c]$.
