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.

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