On the Zeta Functions of Prehomogeneous Vector Spaces for Pair of Simple Algebras
نویسنده
چکیده
In this paper, we consider the prehomogeneous vector space for pair of simple algebras which are k-forms of the D4 type and the E6 type. We mainly study the non-split cases. The main purpose of this paper is to determine the principal parts of the global zeta functions associated with these spaces in the non-split cases. We also give a description of the sets of rational orbits of these spaces, which suggests the expected density theorems arising from the properties of these zeta functions.
منابع مشابه
On the zeta functions of prehomogeneous vector spaces for a pair of simple algebras
— In this paper we consider the prehomogeneous vector space for a pair of simple algebras which are inner forms of the D4 type and the E6 type. We mainly study the non-split cases. The main purpose of this paper is to determine the principal parts of the global zeta functions associated with these spaces when the simple algebras are non-split. We also give a description of the sets of rational ...
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