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December 2013 Multidimensional Shintani Zeta Functions and Zeta Distributions on $\mathbb{R}^d$
Takahiro AOYAMA, Takashi NAKAMURA
Tokyo J. Math. 36(2): 521-538 (December 2013). DOI: 10.3836/tjm/1391177986

Abstract

The class of Riemann zeta distribution is one of the classical classes of probability distributions on $\mathbb{R}$. Multidimensional Shintani zeta function is introduced and its definable probability distributions on $\mathbb{R}^d$ 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 $\mathbb{R}^d$, is also studied.

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Takahiro AOYAMA. Takashi NAKAMURA. "Multidimensional Shintani Zeta Functions and Zeta Distributions on $\mathbb{R}^d$." Tokyo J. Math. 36 (2) 521 - 538, December 2013. https://doi.org/10.3836/tjm/1391177986

Information

Published: December 2013
First available in Project Euclid: 31 January 2014

zbMATH: 1286.11139
MathSciNet: MR3161573
Digital Object Identifier: 10.3836/tjm/1391177986

Subjects:
Primary: 11M
Secondary: 60E

Rights: Copyright © 2013 Publication Committee for the Tokyo Journal of Mathematics

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Vol.36 • No. 2 • December 2013
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