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

1994/08/15 by Yukie, Akihiko
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/9408212

Abstract

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 ∈ 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_x⁰ the connected component of 1 of G_x. We define L₀ to be the set of x in V_k^ss such that G_x⁰ does not have a non-trivial rational character. We study the zeta function for (G,V).

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