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

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 .

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