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

Wenguang Zhai

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

Number Theory 2008-05-13 v1

Authors: Wenguang Zhai

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 .

Keywords

Dirichlet divisor problem error term asymptotic formula power moment analytic number theory

Cite

@article{arxiv.0805.1523,
  title  = {On higher-power moments of $\Delta(x)$(III)},
  author = {Wenguang Zhai},
  journal= {arXiv preprint arXiv:0805.1523},
  year   = {2008}
}

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