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Archiv der Mathematik

, Volume 77, Issue 3, pp 233–240 | Cite as

On the distribution of square-full integers

Article

Abstract.

Let \( A(x) \) be the number of square-full integers \( \leqq x \) and let \( \Delta(x) \) be the error term in the asymptotic formula for \( A(x) \). Under the Riemann hypothesis, we show that \( \Delta(x)\ll x^{{12\over 85}+\varepsilon} \). This improves the earlier results of Zhu and Yu [17], Cao [4, II], Liu [9] and Wu [16], which requires \( 1\over 7 \) in place of \( 12\over 85 \).

Keywords

Error Term Early Result Asymptotic Formula Riemann Hypothesis 

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Copyright information

© Birkhäuser Verlag, Basel 2001

Authors and Affiliations

  • J. Wu
    • 1
  1. 1.Institut Elie Cartan, UMR 7502 UHP-CNRS-INRIA, Université Henri Poincaré (Nancy 1), 54506 Van\oeuvre–lès–Nancy, FranceFrance

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