  There is a natural question to ask whether the rich mathematical theory of
the hyperelliptic curves can be extended to all superelliptic curves. Moreover,
one wonders if all of the applications of hyperelliptic curves such as
cryptography, mathematical physics, quantum computation, diophantine geometry,
etc can carry over to the superelliptic curves. In this short paper we make the
case that the superelliptic curves are exactly the curves that one should
study.
