The theory of prehomogeneous vector spaces is a relatively new
subject although its origin can be traced back through the works of
Siegel to Gauss. This is the first book on this topic, and
represents the author's deep study of prehomogeneous vector spaces.
Here the author's aim is to generalize Shintani's approach from the
viewpoint of geometric invariant theory, and in some special cases
he also determines not only the pole structure but also the
principal part of the zeta function.