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Character sums over squarefree and squarefull numbers. (English) Zbl 1297.11097

In this paper, some upper bounds for sums of characters over squarefree and squarefull numbers in the initial interval are derived from the Burgess bound. Estimates for squarefull numbers are obtained by decomposing such a number in the form \(a^2b^3\) where b is squarefree. The results are used to sharpen results obtained by H. Liu and W. Zhang [J. Math. Kyoto Univ. 45, No. 2, 247–255 (2005; Zbl 1089.11052)] concerning the error term in the distribution of squarefull numbers in arithmetic progressions.

MSC:

11L40 Estimates on character sums

Citations:

Zbl 1089.11052
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References:

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