On higher-power moments of $Δ(x)$(III)

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

2008-05-11

arxiv.org/abs/0805.1523v1

Acta Arith. 118 (2005), 263--281

Mathematics

Number Theory

21 Pages

Scientific paper

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 .

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