  Finite Euler product is known to be one of the classical zeta functions in
number theory. In [1], [2] and [3], we have introduced some multivariable zeta
functions and studied their definable probability distributions on R^d. They
include functions which generate infinitely divisible, not infinitely divisible
characteristic functions and not even to be characteristic functions. In this
paper, we treat some multivariable finite Euler products and show how they
behave in view of such properties.
