On higher-power moments of $\Delta(x)$(III)

descriptionPublicationkeyboard_double_arrow_right Preprint , Article 08 May 2008Publisher:Polish Academy of Sciences (Polska Akademia Nauk - PAN), Institute of Mathematics (Instytut Matematyczny), Warsaw

Authors: Zhai, Wenguang;

arXiv: 0805.1523 , 0805.1270

On higher-power moments of $\Delta(x)$(III)

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Abstract

Let $\Delta(x)$ be the error term of the Dirichlet divisor problem. An asymptotic formula with the error term $O(T^{53/28+\epsilon})$ is established for the integral $\int_1^T\Delta^4(x)dx.$ Similar results are also established for some other well-known error terms in the analytic number theory .

Comment: 21 Pages

Related Organizations

Shandong Normal University
China (People's Republic of)

Keywords

Mathematics - Number Theory, 11N37, 11M06, $\zeta (s)$ and $L(s, \chi)$, Asymptotic results on arithmetic functions, Dirichlet divisor problem, power moments, Riemann zeta-function

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