On the distribution of the zeros of the Riemann zeta function in short intervals
type: Item
instance of: scholarly article
title: On the distribution of the zeros of the Riemann zeta function in short intervals
zbMATH Open document ID: 0705.11048
author: Akio Fujii
published in: Proceedings of the Japan Academy. Series A
publication date: 1990-01-01T00:00:00Z
review text: Let \(s(t)=(1/\pi)\arg \zeta (+it)\). Assuming the Riemann Hypothesis the author obtains an asymptotic formula for \(\int^{T}_{0}(s(t+\Delta)- s(t))^ 2dt\), where \(\Delta =o(1)\). The method is based on \textit{D. A. Goldston}'s paper [J. Number Theory 27, 149-177 (1987; Zbl 0618.10037)] and the result refines a previous result of the author [Bull. Am. Math. Soc. 81, 139-142 (1975; Zbl 0297.10026)].
Mathematics Subject Classification ID: 11M26
zbMATH DE Number: 4156559
zbMATH Keywords: Riemann zeta function
zbMATH Keywords: Riemann Hypothesis
reviewed by: A. Perelli
MaRDI profile type: Publication
full work available at URL: pjaa.66.75
OpenAlex ID: W2069505975
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DOI: 10.3792/PJAA.66.75
description: scientific article; zbMATH DE number 4156559