Multidimensional Shintani zeta functions and zeta distributions on R^d

TL;DR

This paper introduces multidimensional Shintani zeta functions, explores their associated probability distributions on R^d, and examines their connection to multidimensional Euler products and infinitely divisible distributions.

Contribution

It defines a new class of probability distributions on R^d based on multidimensional Shintani zeta functions and studies their properties and relations to existing distributions.

Findings

Includes fundamental distributions like binomial and Poisson within the new class.

Establishes a connection between Shintani zeta functions and multidimensional Euler products.

Shows these distributions are related to multidimensional infinitely divisible distributions.

Abstract

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.