Limit theorem for the Riemann zeta-function on the critical line. III
type: Item
instance of: scholarly article
title: Limit theorem for the Riemann zeta-function on the critical line. III
zbMATH Open document ID: 0685.10028
DOI: 10.1007/BF00966497
published in: Lithuanian Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: [For parts I, II, cf. ibid. 27, No. 1, 113--132 (1987; Zbl 0641.10031); ibid. 27, No. 3, 489--500 (1987; Zbl 0641.10032).] Es sei \(\text{mes }A\) das Lebesguesche Maß einer L-meßbaren Menge \(A\) und für \(T>e\), \(\sigma>0\) \[ F_{\sigma,T}(x)=(1/T)\text{ mes}\{t\in [0,T] | \mid | \zeta (\sigma+it)|^{\epsilon_ T}<x\} \] mit \(\epsilon_ T=(1/2 \ln \ln T)^{-1/2}\). Der Verf. gibt einen neuen Beweis von \[ \lim_{T\to \infty}F_{1/2,T}(x)= (1/\sqrt{2\pi})\int^{\ln x}_{-\infty}e^{-u^ 2/2}\, du\text{ für }x>0 \] mit Hilfe eines analogen Grenzwertsatzes für \(F_{\sigma_ T,T}(x)\), wo \(\sigma_ T\) eine spezielle Funktion mit \(\sigma_ T\to~1/2\) \((T\to \infty)\) bedeutet [vgl. Mat. Sb., Nov. Ser. 135(177), No. 1, 3--11 (1988; Zbl 0649.10026)].
Mathematics Subject Classification ID: 11M06
Mathematics Subject Classification ID: 11K99
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 4122071
zbMATH Keywords: limit theorem
zbMATH Keywords: Riemann zeta-function
zbMATH Keywords: critical
zbMATH Keywords: line
author: Antanas Laurinčikas
reviewed by: Wolfgang Haneke
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00966497
OpenAlex ID: W2011232202
description: scientific article; zbMATH DE number 4122071