# Behaviors of multivariable finite Euler products in probabilistic view

Takahiro Aoyama, Takashi Nakamura

Research output: Contribution to journalArticle

3 Citations (Scopus)

### Abstract

The finite Euler product is known one of the classical zeta functions in number theory. In ,  and , we have introduced some multivariable zeta functions and studied their definable probability distributions on Rd. They include functions which generate infinitely divisible, not infinitely divisible characteristic functions and not even to be characteristic functions. In this paper, we treat some multivariable finite Euler products and show how they behave in view of such properties.

Original language English 1691-1700 10 Mathematische Nachrichten 286 17-18 https://doi.org/10.1002/mana.201200151 Published - Dec 2013 Yes

### Fingerprint

Euler Product
Infinitely Divisible
Characteristic Function
Riemann zeta function
Number theory
Probability Distribution

### Keywords

• Characteristic function
• Finite Euler product
• Infinite divisibility

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

In: Mathematische Nachrichten, Vol. 286, No. 17-18, 12.2013, p. 1691-1700.

Research output: Contribution to journalArticle

Aoyama, Takahiro ; Nakamura, Takashi. / Behaviors of multivariable finite Euler products in probabilistic view. In: Mathematische Nachrichten. 2013 ; Vol. 286, No. 17-18. pp. 1691-1700.
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