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

By Wenguang Zhai. 2008

49 citations recorded by the source corpus.

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 .

Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a783bbfdca3a8d1f7df66a107e1abdfe14cac70a