Inhomogeneous Diophantine approximation in the coprime setting

Svetlana Jitomirskaya, Wencai Liu

Given $n\in N$ and $x,\gamma \in R$, let \begin{equation*} ||γ-nx||^\prime=\min\{|γ-nx+m|:m\in Z, \gcd (n,m)=1\}, \end{equation*} %where $(n,m)$ is the largest common divisor of $n$ and…