Zeta functions of classical groups and their friendly ghosts

The zeta functions of the classical reductive groups in general have natural boundaries. We introduce in this Note the concept of the ghost zeta function which exists for any zeta function expressed as an Euler product of uniformly rational functions. We give an explicit description of the host zeta functions for the classical groups and prove that they are meromorphic functions. (C) Academie des Sciences/Elsevier, Paris.