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

Number Theory 2016-09-21 v1
Authors: Wenguang Zhai
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Abstract

Let Δ(x)\Delta(x) be the error term of the Dirichlet divisor problem. The asymptotic formula of the integral ∫1TΔk(x)dx\int_1^T\Delta^k(x)dx is established for any integer 3≤k≤93\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.

Keywords

Dirichlet divisor problem error term higher-power moments asymptotic formula analytic number theory unified method

Cite

@article{arxiv.0805.1270,
  title  = {On higher-power moments of $\Delta(x)$(II)},
  author = {Wenguang Zhai},
  journal= {arXiv preprint arXiv:0805.1270},
  year   = {2016}
}

Comments

23 Pages, 20 references

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