  The class of Riemann zeta distribution is one of the classical classes of
probability distributions on R. Multidimensional Shintani zeta function is
introduced and its definable probability distributions on R^d are studied. This
class contains some fundamental probability distributions such as binomial and
Poisson distributions. The relation with multidimensional polynomial Euler
product, which induces multidimensional infinitely divisible distributions on
R^d, is also studied.
