The fundamental theorem of prehomogeneous vector spaces modulo (With an appendix by F. Sato)
For a number field with ring of integers , we prove an analogue over finite rings of the form of the fundamental theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where is a big enough prime ideal of and . In the appendix, F.Sato gives an application of the Theorems 1.1, 1.3 and the Theorems A, B, C in J.Denef and A.Gyoja [, Compos. Math., (1998), 237–346] to the functional equation of -functions of Dirichlet type associated with prehomogeneous...