Small gaps between the Piatetski-Shapiro primes

Li, Hongze; Pan, Hao

doi:10.1090/tran/8205

Small gaps between the Piatetski-Shapiro primes
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Trans. Amer. Math. Soc. 373 (2020), 8463-8484 Request permission

Abstract:

Suppose that $1<c<9/8$. For any $m\geq 1$, there exist infinitely many $n$ such that \begin{equation*} \{[n^c],\ [(n+1)^c],\ \ldots ,\ [(n+k_0)^c]\} \end{equation*} contains at least $m+1$ primes, if $k_0$ is sufficiently large (only depending on $m$ and $c$).

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