On the correlations of directions in the Euclidean plane
  We study the correlations of directions $P_0 P$ in the Euclidean plane, where $P_0$ is a point in a fixed disc, $P$ is an integer lattice point in the square $[-Q,Q]^2$, and $Q\to \infty$. 
Florin P. Boca and Alexandru Zaharescu