AI 中文总结
该数论研究将Piatetski-Shapiro素数相关结果中殆素数的素因子上限从8优化至7，针对0.98353到1之间的$\u03b3$，证明存在无穷多符合条件的素数。
AI 中文摘要
记$\u2119_r$为最多含$r$个素因子（计重数）的殆素数。本文证明，对任意固定的$0.98353<\u03b3<1$，存在无穷多形如$p=[n^{1/\u03b3}]$的素数，其中$n$为殆素数$\u2119_7$。该结果改进了Baker、Banks、Guo和Yeager的先前结论，他们证明当$\u03b3$接近1时，存在无穷多素数$p$满足$p=[n^{1/\u03b3}]$且$n\u2208\u2119_8$。
英文摘要
Denote by $\mathcal{P}_r$ an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this manuscript, it is established that, for any fixed $0.98353<γ<1$, there exist infinitely many primes of the form $p=[n^{1/γ}]$, where $n$ is an almost-prime $\mathcal{P}_7$. This result constitutes an improvement upon the previous result of Baker, Banks, Guo and Yeager [1], who showed that there exist infinitely many primes $p$ such that $p=[n^{1/γ}]$ with $n\in\mathcal{P}_8$ for $γ$ near to one.
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