Generalized character sums associated to regular prehomogeneous vector spaces
Abstract
In this paper we consider the analogue of the Sato's functional equation for the prehomogeneous vector spaces over finite fields. The corresponding character sums depend on a relative invariant on such a space and an irreducible representation of the group of components of the stabilizer of a generic point. The proof is based on the PicardLefschetz formula in $l$adique cohomology.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 1999
 arXiv:
 arXiv:math/9906173
 Bibcode:
 1999math......6173K
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 AMSLatex, 16 pages, new theorem added