Abstract
There exist not many treatable multivariable functions with respect to multidimensional discrete distributions. In this paper, we pick up multidimensional finite Euler products and show when they can generate characteristic functions. Moreover, the infinite divisibility of them are studied as well as non-infinite divisibility which are rarely seen in multidimensional discrete case with infinitely many mass points. The relation between series representations of zeta functions is also studied by adjusting to the Shintani zeta type.
