Diophantine approximation on lines in \mathbb{C}^2 with Gaussian prime constraints - enhanced version

Abstract

We study the problem of Diophantine approximation on lines in $\mathbb{C}^2$ with numerators and denominators restricted to Gaussian primes. To this end, we develop analogs of well-known results on small fractional parts of $p\gamma$, $p$ running over the primes and $\gamma$ being a fixed irrational, for Gaussian primes.