The number of Piatetski-Shapiro primes in short intervals

We study the distribution of Piatetski-Shapiro primes, or primes of the form $[n^c]$, in short intervals of length $x^{\theta}$. We give an asymptotic formula of the number of such primes in short intervals under certain restrictions on $\theta$ and $c$, which is better than a previous result of Guo and Guo (2026) when $\theta > \frac{11}{12}$. We present two proofs of our Theorem based on different sieve decompositions, using Buchstab's identity and the Heath-Brown--Linnik identity respectively.