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

Abstract

Let $\Delta (x)$ be the error term of the Dirichlet divisor problem. The asymptotic formula of the integral ${\int }_1^T{\Delta }^k(x)dx$ is established for any integer $3\le k\le 9$ by an unified method. Similar results are also established for some other well-known error terms in the analytic number theory.

23 Pages, 20 references

Cited by in corpus (4)

• On the Tong-type identity and the mean square of the error term for an extended Selberg class
• On the Rankin-Selberg problem: higher power moments of the Riesz mean error term
• On the Fourth Power Moment of Fourier Coefficients of Cusp Form
• On the error term in Weyl's law for the Heisenberg manifolds (II)