Fundamental domains
 
Zeev Rudnick proved that QUE implies that the zeros of the associated cusp forms also are equidistributed in the (hyperbolic) upper halfplane. So this picture is an illustration of the result of Holowinsky and Soundararajan.
The standard fundamental domain for SL(2,Z) is the set of points
in the upper halfplane. This is the shaded region in the picture below. The picture above shows a different (but equivalent) fundamental domain. It was chosen because in the usual fundamental domain the points near the cusp at infinity are very far from the bulk of the points (in the Euclidean metric). But if you would like to see the above picture transformed into the standard fundamental domain, just scan down the left edge of this webpage. The upper halfplane tiled by fundamental domains for SL(2,Z):
