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