The Atkinson formula for \(L\)-functions near the critical line
type: Item
instance of: scholarly article
title: The Atkinson formula for \(L\)-functions near the critical line
zbMATH Open document ID: 0827.11053
DOI: 10.1007/BF00995988
published in: Lithuanian Mathematical Journal
publication date: 1995-09-18T00:00:00Z
review text: This paper brings forth generalizations of the author's work [Liet. Mat. Rink. 33, No. 3, 302-313 (1993; see the review above)] on Atkinson's formula (for the mean square of \(\zeta ({1\over 2}+ it)\) near the critical line) to \(L\)-functions. The author uses the methods and ideas from the work of \textit{T. Meurman} [Acta Arith. 47, 351-370 (1986; Zbl 0604.10023)] to obtain the analogue of Meurman's results on the line \(\sigma_T= {1\over 2}+ {1\over {l_T}}+ it\), \(l_T>0\) and \(l_T\) monotonically tends to \(\infty\) as \(T\to \infty\). There are three theorems, providing an explicit expression and bound for the error-term function \(E(\sigma_T, q,T)\) (defined precisely in the text), and the quantity \[ \sum_{\chi\pmod q} \int_T^{T+H} \bigl|L(\sigma_T+ it, \chi) \bigr|^2 dt, \qquad H\gg 1. \]
reviewed by: Aleksandar Ivić
Mathematics Subject Classification ID: 11M06
zbMATH DE Number: 794501
zbMATH Keywords: Dirichlet characters
zbMATH Keywords: Atkinson's formula
zbMATH Keywords: mean square
zbMATH Keywords: critical line
zbMATH Keywords: \(L\)-functions
zbMATH Keywords: error-term
author: Antanas Laurinčikas
MaRDI profile type: Publication
cites work: The mean-value of the Riemann zeta function
cites work: The Atkinson formula near the critical line. II
cites work: A generalization of Atkinson's formula to L-functions
description: scientific article; zbMATH DE number 794501