On the distribution of $\alpha p^2$ modulo one with prime $p$ of a special form

Fei Xue, Jinjiang Li, Min Zhang

Let ${\mathcal{P}}_r$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, it is proved that for $α\in\mathbb{R}\backslash\mathbb{…