On a joint limit distribution for the Riemann zeta-function in the space of analytic functions
type: Item
instance of: scholarly article
title: On a joint limit distribution for the Riemann zeta-function in the space of analytic functions
zbMATH Open document ID: 1023.11042
DOI: 10.1023/A:1021786525108
author: R. Steuding
published in: Lithuanian Mathematical Journal
publication date: 2003-05-19T00:00:00Z
review text: This paper is a continuation of the author's article [Lith. Math. J. 42, No. 3, 308-314 (2002; Zbl 1023.11041)], and the same applies for the reviews. The subject of this paper is the explicit form of the limit measure which was described in the paper and its review cited above. Denote by \(\gamma\) the unit circle in the complex plane, and define \(\Omega = \prod_{p}\gamma_{p}\) where the product is over all prime numbers and \(\gamma_{p} = \gamma\). Let \(\omega(p)\) stand for the projection of \(\omega\in \Omega\) onto \(\gamma_{p}\). Define on \((\Omega, \mathcal B (\Omega))\) the \(H^{r}(D)\)-valued random element \[ \zeta(s,\omega) = \Biggl( \prod_{p} \biggl(1-{\omega^{k_{1}}(p)\over p^{s}} \biggr)^{-1}, \ldots , \prod_{p} \biggl(1- {\omega^{k_{r}}(p)\over p^{s}}\biggr)^{-1}\Biggr). \] Then the distribution of \(\zeta(s,\omega)\), denoted by \(P_{\zeta}\), is the limit probability measure sought after.
Mathematics Subject Classification ID: 11M06
Mathematics Subject Classification ID: 11K99
zbMATH DE Number: 1912635
zbMATH Keywords: Riemann zeta-function
zbMATH Keywords: probability measure
zbMATH Keywords: limit distribution
reviewed by: C. Y. Yildirim
MaRDI profile type: Publication
full work available at URL: a:1021786525108
OpenAlex ID: W2912897617
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description: scientific article; zbMATH DE number 1912635