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A probabilistic study on the value-distribution of Dirichlet series attached to certain cusp forms

Published online by Cambridge University Press:  22 January 2016

Kohji Matsumoto
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The existence of the asymptotic probability measure of the Riemann zeta-function was proved in Bohr-Jessen’s classical paper [3] [4].

Let s = σ + it be a complex variable, ζ(s) the Riemann zeta-function, and R an arbitrary rectangle with the edges parallel to the axes. Then, for any σ0 > ½ and T > 0, the set

is Jordan measurable, and we denote the Jordan measure of this set by V(T, R; ξ). Then, Bohr-Jessen’s main result asserts the existence of the limit

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 116 , December 1989 , pp. 123 - 138
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

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