On the zeta functions of prehomogeneous vector spaces for pair of simple algebras

Details On the zeta functions of prehomogeneous vector spaces for pair of simple algebras On the zeta functions of prehomogeneous vector spaces for pair of simple algebras

2004-03-16

arxiv.org/abs/math/0403253v1

Mathematics

Number Theory

20 pages, AMS LaTeX

Scientific paper

In this paper, we consider the prehomogeneous vector space for pair of simple algebras which are $k$-forms of the $D_4$ type and the $E_6$ 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.

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