Diophantine approximation with prime denominator in quadratic number fields under GRH

Stephan Baier, Sourav Das, Esrafil Ali Molla

Matomäki proved that if $\hat{I}\pm \in \mathbb{R}$ is irrational, then there are infinitely many primes $p$ such that $|\hat{I}\pm -a/p|\le p^{-4/3+\epsilon }$ for a suitable integer a. In this…