Geodesic
On some mean values for the divisor function and the Riemann zeta-function
Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 150-162

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Let $\Delta (x)$ and $E(x)$ denote respectively the error terms in the summatory formula for the divisor function and in the mean square formula for $\zeta (s)$ on the critical line. We consider some general mean values for $\Delta (x)$ and $E(x)$ and discover interesting differences between these two functions. In particular, this yields evidence that $E(x)$ is more negative than $\Delta (x)$. 
@article{TRSPY_2017_296_a11,
     author = {Kar-Lun Kong and Kai-Man Tsang},
     title = {On some mean values for the divisor function and the {Riemann} zeta-function},
     journal = {Informatics and Automation},
     pages = {150--162},
     publisher = {mathdoc},
     volume = {296},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a11/}
}
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Kar-Lun Kong; Kai-Man Tsang. On some mean values for the divisor function and the Riemann zeta-function. Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 150-162. http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a11/