On the subtle effect of a zenith dependent angular resolution over the coverage

In this short note, we describe a Monte Carlo based study of the small distortions introduced into the coverage when one has a detector whose angular resolution (AR) varies with the zenith angle. The effect is such that it introduces fake hot spots into the coverage maps, corresponding to events measured with better AR (smaller \sigma). A good coverage, however, should exhibit such distortions, since their origin is local, in order to the excess maps to retain only true sky anisotropies.