Chaos expansion of uniformly distributed random variables and application to number theory
Volume 8, Issue 2 (2021), pp. 275–289
Pub. online: 26 March 2021
Type: Research Article
Open Access
Open Access
Received
29 January 2021
29 January 2021
Revised
13 February 2021
13 February 2021
Accepted
20 February 2021
20 February 2021
Published
26 March 2021
26 March 2021
Abstract
The chaos expansion of a random variable with uniform distribution is given. This decomposition is applied to analyze the behavior of each chaos component of the random variable $\log \zeta $ on the so-called critical line, where ζ is the Riemann zeta function. This analysis gives a better understanding of a famous theorem by Selberg.
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