Zeta functions in several variables associated with prehomogeneous vector spaces, II. A convergence criterion
Fumihiro Satō · Proceedings of the Japan Academy Series A Mathematical Sciences · 1981
This article is a continuation of [2].Here we present a sufficient condition of the convergence of zeta functions introduced in the previ- ous paper.We keep the notation and the assumptions in [2] except (A.3).. Let H be the identity component (in the Zariski topology) of the group {g e G; z(g)= 1 for all Z e X,(G)}.We consider the following four conditions:(I) For any t=(t, ..., tn) e (C)n, H acts transitively on(W) For any x e V-So, the Tamagawa number of Hx does not exceed some positive constant independent of x.