COMPUTATION OF CHARACTER SUMS AND APPLICATIONS TO PREHOMOGENEOUS VECTOR SPACES 1 with an appendix ” L - FUNCTIONS OF PREHOMOGENEOUS VECTOR SPACES
نویسنده
چکیده
For an arbitrary number field K with ring of integers OK , we prove an analogue over finite rings of the form OK/p 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 OK and m > 1. In the appendix, F. Sato gives an application of the Theorems 1.2 and 1.5 (and Theorems A, B, C in [4]) to the functional equation of L-functions of Dirichlet type associated with prehomogeneous vector spaces. §
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