On generalized Igusa local zeta functions associated to simple Chevalley K-groups under the adjoint representation

抄録

The purpose of this paper is to provide the reader with an introduction to the theory of generalized Igusa local zeta functions associated to irreducible matrix groups. As an application, the generalized Igusa local zeta function Z_K(s) associated to the simple Chevalley K-groups of type B_{l}, C_{l}, D_{l}, E₆, E₇, E₈, F₄ and G₂ under the adjoint representation is explicitly exhibited as a rational function satisfying a certain functional equation.