A Remark on the Piatetski-Shapiro-Hua Theorem

In this paper, we prove that for any fixed $205\mathrm{/}243<\gamma ⩽1$, every sufficiently large $N$ satisfying $N\equiv 5(\mathrm{m}\mathrm{o}\mathrm{d}24)$ can be represented as five squares of primes with one prime in ${\mathcal{P}}_{\gamma }$, which improves the previous result of Zhang and Zhai.