On higher-power moments of $Δ(x)$(II)

Details On higher-power moments of $Δ(x)$(II) On higher-power moments of $Δ(x)$(II)

2008-05-09

arxiv.org/abs/0805.1270v1

Acta Arith. Vol.{\bf 114}(2004), 35-54

Mathematics

Number Theory

23 Pages, 20 references

Scientific paper

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 $3\leq k\leq 9$ by an unified method. Similar results are also
established for some other well-known error terms in the analytic number theory.

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