Multidimensional Shintani zeta functions and zeta distributions on R^d

Takahiro Aoyama; Takashi Nakamura

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arXiv · 1204.4042

Multidimensional Shintani zeta functions and zeta distributions on R^d

Takahiro Aoyama·Takashi Nakamura

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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.

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Takahiro Aoyama, Takashi Nakamura. 2012-04-18. Multidimensional Shintani zeta functions and zeta distributions on R^d. https://arxiv.org/abs/1204.4042

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