On the distribution of $\alpha p^{\gamma }+\beta$ modulo one

Alexander Dunn

Let $\Vert \cdot \Vert$ denote the minimum distance to an integer. For $0<\gamma <1$, $\theta >0$ and $(\alpha ,\beta )\in \mathbb{R}\setminus \{0\}\times \mathbb{R}$ we study when \begin{equation*} \|αp^γ+…