  We determine the positive integers a,b and the prime powers q for which the
word map w(x,y)=x^ay^b is surjective on the group PSL(2,q) (and SL(2,q)). We
moreover show that this map is almost equidistributed for the family of groups
PSL(2,q) (and SL(2,q)). Our proof is based on the investigation of the trace
map of positive words.
