  We give the distribution of points on smooth superelliptic curves over a
fixed finite field, as their degree goes to infinity. We also give the
distribution of points on smooth m-fold cyclic covers of the line, for any m,
as the degree of their superelliptic model goes to infinity. This builds on
previous work of Kurlberg, Rudnick, Bucur, David, Feigon, and Lalin for p-fold
cyclic covers, but the limits taken differ slightly and the resulting
distributions are interestingly different.
