On the Seventh Power Moment of $\Delta(x)$

Jinjiang Li

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arXiv · 1601.05515

On the Seventh Power Moment of $\Delta(x)$

Jinjiang Li

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Abstract

Let $\Delta(x)$ be the error term of the Dirichlet divisor problem. In this paper, we establish an asymptotic formula of the seventh-power moment of $\Delta(x)$ and prove that \begin{equation*} \int_2^T \Delta^7(x)\mathrm{d}x= \frac{7(5s_{7;3}(d)-3s_{7;2}(d)-s_{7;1}(d))}{2816\pi^7}T^{11/4}+O(T^{11/4-\delta_7+\varepsilon}) \end{equation*} with $\delta_7=1/336,$ which improves the previous result.

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Jinjiang Li. 2016-01-21. On the Seventh Power Moment of $\Delta(x)$. https://arxiv.org/abs/1601.05515

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