A mean value theorem for Dirichlet series and a general divisor problem
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.
scientific article; zbMATH DE number 1798917