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

Raf Cluckers, Adriaan Herremans (2007)

Bulletin de la Société Mathématique de France

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, 1.3 and the Theorems A, B, C in J.Denef and A.Gyoja [Character sums associated to prehomogeneous vector spaces, Compos. Math., 113(1998), 237–346] to the functional equation of L -functions...

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