ON GENERALIZED IGUSA LOCAL ZETA FUNCTIONS ASSOCIATED TO SIMPLE CHEVALLEY K-GROUPS UNDER THE ADJOINT REPRESENTATION

摘要

The purpose of this paper is to provide the reader with an introduction to the thory of generalized Igusa local zeta functions associated to irreducible matrix groups. As an application, the generalized Igusa local zeta function Zk(s) associated to the simple Chevalley K-groups of type Bl,Cl,Dl,E_6,E_7,E_8,F_4 and G_2 under the adjoint representation is explicitly exhibited as a rational function satisfying a certain functional equation.