On the convergence of the zeta function for certain prehomogeneous vector spaces
Representation Theory
2016-09-06 v1
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 \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).
Keywords
Cite
@article{arxiv.math/9408212,
title = {On the convergence of the zeta function for certain prehomogeneous vector spaces},
author = {Akihiko Yukie},
journal= {arXiv preprint arXiv:math/9408212},
year = {2016}
}