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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

Trudy Mat. Inst. Steklova, 2017 Volume 296, Pages 150–162 (Mi tm3793)

On some mean values for the divisor function and the Riemann zeta-function

Kar-Lun Kong, Kai-Man Tsang

Department of Mathematics, University of Hong Kong, Hong Kong SAR, China

Abstract: 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 $\Delta (x)$.

UDC: 511.335+511.338+511.352

Received: May 22, 2016

DOI: 10.1134/S0371968517010125


 English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 296, 142–153

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