Let ∆(x) be the error term of the Dirichlet divisor problem. An asymptotic formula with the error term O(T 53/28+ε ) is established for the integral T 1 ∆ 4 (x)dx. Similar results are also established for some other well-known error terms in the analytic number theory .
Let ∆(a, b; x) denote the error term of the general two-dimensional divisor problem. In this paper we shall study the relation between the discrete mean value n≤T ∆ 2 (a, b; n) and the continuous mean value T 1 ∆ 2 (a, b; x)dx.
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