Exponential sums over Piatetski-Shapiro primes in arithmetic progressions

Let $\gamma <1<c$ and $19(c-1)+171(1-\gamma )<9$. In this paper, we establish an asymptotic formula for exponential sums over Piatetski-Shapiro primes $p=[n^{1\mathrm{/}\gamma }]$ in arithmetic progressions.