Piatetski-Shapiro Primes in a Beatty Sequence

Abstract

Let $\alpha ,\beta$ be real numbers such that $\alpha >1$ is irrational and of finite type, and let $c$ be a real number in the range $1<c<\frac{14}{13}$. In this paper, it is shown that there are infinitely many Piatetski-Shapiro primes $p=\lfloor n^c\rfloor$ in the non-homogenous Beatty sequence $(\lfloor \alpha m+\beta \rfloor {)}_{m=1}^{\infty }$.