On the convergence of the zeta function for certain prehomogeneous vector spaces

Details On the convergence of the zeta function for certain prehomogeneous vector spaces On the convergence of the zeta function for certain prehomogeneous vector spaces

1994-08-15

arxiv.org/abs/math/9408212v1

Mathematics

Representation Theory

Scientific paper

Let (G,V) be an irreducible prehomogeneous vector space defined over a number field k, P in k[V] a relative invariant polynomial, and X a rational character of G such that P(gx)=X(g)P(x). Let V_k^{ss}={x \in V_k such that P(x) is not equal to 0}. For x in V_k^{ss}, let G_x be the stabilizer of x, and G_x^0 the connected component of 1 of G_x. We define L_0 to be the set of x in V_k^{ss} such that G_x^0 does not have a non-trivial rational character. We study the zeta function for (G,V).

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