At the end of this very nice post:

http://blogs.ethz.ch/kowalski/2012/05/21/who-needled-buffon/

E. Kowalski talks about the equidistribution of the points $\frac{j+i}{N}$ when $j=1,\dots,N$ and $N$ tends to $\infty$ in the fundamental domain of $SL_2(R)/SL_2(Z)$. He says that it "follows here most easily from non-trivial bounds on Hecke eigenvalues of Maass cusp forms".

Can anyone fill in the details of give a good reference? any related thoughts will also be appreciated!