Mean-value theorem of Riemann zeta-function over short intervals
type: Item
instance of: scholarly article
title: Mean-value theorem of Riemann zeta-function over short intervals
zbMATH Open document ID: 0786.11054
published in: Journal of Number Theory
publication date: 1994-05-09T00:00:00Z
review text: Assuming the Riemann hypothesis, the authors obtain an asymptotic formula for the mean-square of \(\zeta(\sigma+it)\) over \((T,T+H)\), provided \(1/2+ c/\log\log T\leq\sigma\leq 1-\delta\) and \(Y\leq H\leq T\), where \(Y=\exp((\log T)^{2-2\sigma})\) and \(c,\delta>0\). The proof is based on a mean-value theorem for Dirichlet polynomials.
Mathematics Subject Classification ID: 11M06
zbMATH DE Number: 483992
zbMATH Keywords: asymptotic formula
zbMATH Keywords: mean-square of Riemann zeta-function
zbMATH Keywords: mean-value theorem
zbMATH Keywords: Dirichlet polynomials
author: Ayyadurai Sankaranarayanan
author: K. Srinivas
reviewed by: A. Perelli
MaRDI profile type: Publication
full work available at URL: jnth.1993.1081
OpenAlex ID: W2004863186
DOI: 10.1006/JNTH.1993.1081
description: scientific article; zbMATH DE number 483992