Diophantine approximation with primes in an arithmetic progression

D. Mazumder, J. Sivaraman

Let $\alpha \in \mathbb{R}\setminus \mathbb{Q}$, $\beta \in \mathbb{R}$, $N\in {\mathbb{R}}_{\ge 1}$ and $\Delta \in (0,1/2)$. For any real $y$, let $\Vert y\Vert$ denote the distance from $y$ to the nearest in…