The fundamental theorem of prehomogeneous vector spaces modulo $p^m$ (With an appendix by F. Sato)

Abstract

Abstract. -For a number field K with ring of integers O K , we prove an analogue over finite rings of the form O K /P m of the fundamental theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where P is a big enough prime ideal of O K and m > 1. In the appendix, F. Sato gives an application of the Theorems 1.1, 1.