Weighted limit theorem for the Riemann zeta function in the space of analytic functions
type: Item
instance of: scholarly article
title: Weighted limit theorem for the Riemann zeta function in the space of analytic functions
zbMATH Open document ID: 0837.11048
DOI: 10.1007/BF02333415
author: Yanyan Li
published in: Lithuanian Mathematical Journal
publication date: 1995-11-07T00:00:00Z
review text: Es sei \(B(S)\) die Menge der Borelschen Mengen eines topologischen Raums \(S\). Für eine offene Menge \(G \subset \mathbb{C}\) sei \(H(G)\) der Raum der auf \(G\) analytischen Funktionen, der mit der Topologie der gleichmäßigen Konvergenz auf kompakten Teilmengen von \(G\) versehen ist. Es sei \(D_1 = \{s \in \mathbb{C} : {1 \over 2} < \text{Re} (s) < 1\}\), \(D_2 = \{s \in \mathbb{C} : \text{Re} (s) > 1\}\). Die Verfasser beweisen als Analogon eines Satzes von \textit{A. Laurinčikas} [Lith. Math. J. 33, 234--242 (1993); translation from Liet. Mat. Rink. 33, 302--313 (1993; Zbl 0827.11052)] die schwache Konvergenz entsprechender auf \(B(H(D_j))\) \((j = 1,2)\) definierter Wahrscheinlichkeitsmaße. Der Beweis beruht auf einer Methode von \textit{B. Bagchi} [The statistical behavior and universality properties of the Riemann zeta-function and other allied Dirichlet series, Ph. D. Thesis, Indian Stat. Institut, Calcutta (1981); see also Math. Z. 181, 319--334 (1982; Zbl 0489.10035)].
Mathematics Subject Classification ID: 11M06
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 11K99
zbMATH DE Number: 813136
zbMATH Keywords: weighted limit theorem
zbMATH Keywords: space of analytic functions
zbMATH Keywords: weak convergence of probability measures
zbMATH Keywords: Riemann zeta-function
reviewed by: Wolfgang Haneke
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 813136