Piatetski-Shapiro primes in a Beatty sequence (Q2352022)

Let \(\alpha>1\) be irrational and of finite type. Suppose that \(\beta\in \mathbb{R}\) and \(c\in\left(1,\tfrac{14}{13}\right)\). In this paper it is proved that there are infinitely many Piatetski-Shapiro primes \(p=\lfloor n^c\rfloor\) in the non-homogeneous Beatty sequence \((\lfloor\alpha m+\beta\rfloor)_{m=1}^{\infty}\).