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Generalized character sums associated to regular prehomogeneous vector spaces

David Kazhdan·Alexander Polishchuk
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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 Picard-Lefschetz formula in $l$-adique cohomology.

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David Kazhdan, Alexander Polishchuk. 1999-08-05. Generalized character sums associated to regular prehomogeneous vector spaces. https://arxiv.org/abs/math/9906173

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