On the Seventh Power Moment of $Δ(x)$

Let $Δ(x)$ be the error term of the Dirichlet divisor problem. In this paper, we establish an asymptotic formula of the seventh-power moment of $Δ(x)$ and prove that \begin{equation*} \int_2^T Δ^7(x)\mathrm{d}x= \frac{7(5s_{7;3}(d)-3s_{7;2}(d)-s_{7;1}(d))}{2816π^7}T^{11/4}+O(T^{11/4-δ_7+\varepsilon}) \end{equation*} with $δ_7=1/336,$ which improves the previous result.

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