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Zeta distributions generated by multidimensional polynomial Euler products with complex coefficients
TLDR
In this article, the authors considered multidimensional polynomial Euler products with complex coefficients and gave necessary and sufficient conditions for them to generate infinitely divisible, quasi-infinitely divisible but not even characteristic functions by using Baker's theorem.Abstract:
In the present paper, we treat multidimensional polynomial Euler products with complex coefficients on ${\mathbb{R}}^d$. We give necessary and sufficient conditions for the multidimensional polynomial Euler products to generate infinitely divisible, quasi-infinitely divisible but non-infinitely divisible or not even characteristic functions by using Baker's theorem. Moreover, we give many examples of zeta distributions on ${\mathbb{R}}^d$ generated by the multidimensional polynomial Euler products with complex coefficients. Finally, we consider applications to analytic number theory.read more
Citations
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Lévy processes and infinitely divisible distributions
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
Journal ArticleDOI
Transcendental number theory, by Alan Baker. Pp. x, 147. £4·90. 1975. SBN 0 521 20461 5 (Cambridge University Press)
TL;DR: In this article, the authors give a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients, and their study has developed into a fertile and extensive theory enriching many branches of pure mathematics.
Journal ArticleDOI
Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.)
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
References
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TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
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TL;DR: The Mathematics 160 course at the California Institute of Technology as discussed by the authors was the first volume of a two-volume textbook which evolved from a course (Mathematics 160) offered at the University of California during the last 25 years.
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Lévy processes and infinitely divisible distributions
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
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