A mean value theorem for Dirichlet series and a general divisor problem
type: Item
instance of: scholarly article
title: A mean value theorem for Dirichlet series and a general divisor problem
zbMATH Open document ID: 1022.11047
author: Shigeru Kanemitsu
author: Yoshio Tanigawa
author: Ayyadurai Sankaranarayanan
published in: Monatshefte für Mathematik
publication date: 2002-09-10T00:00:00Z
review text: This work continues the researches of the first two authors [Jia, Chaohua (ed.) et al., Analytic number theory, Kluwer Dev. Math. 6, 205-221 (2002; Zbl 1023.11049)]. The authors consider the mean value formula for general Dirichlet series and derive the sum formula for its coefficients. The improvement of Landau's clasical results is established for the general divisor function. They also obtain the asymptotic behaviour of the mean value when \(\sigma\) is near the abscissa of absolute convergence. Applying their results to known zeta-functions the authors improve on \textit{A. Ivić's} [Theorem 8.5, The Riemann zeta-function, New York: Wiley (1985; Zbl 0556.10026)] estimates for eighth, tenth and twelfth moments of the Riemann zeta-function and also on \textit{K. Chandrasekharan} and \textit{R. Narasimhan}'s [Math. Ann. 152, 30-64 (1963; Zbl 0116.27001)] mean square estimate for the Dedekind zeta-function when \(\sigma\) is near to 1.
reviewed by: Ramūnas Garunkštis
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11M41
zbMATH DE Number: 1798917
zbMATH Keywords: Dirichlet series
zbMATH Keywords: general divisor problem
zbMATH Keywords: mean value theorem
MaRDI profile type: Publication
full work available at URL: s006050200031
OpenAlex ID: W1994823796
DOI: 10.1007/S006050200031
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description: scientific article; zbMATH DE number 1798917