Cao, Zhai: The distribution of square-free numbers of the form $[n^c]$

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Xiaodong Cao; Wenguang Zhai
The distribution of square-free numbers of the form $[n^c]$
Journal de théorie des nombres de Bordeaux, 10 no. 2 (1998), p. 287-299, doi: 10.5802/jtnb.229
Article PDF | Reviews MR 1828246 | Zbl 0926.11066
Keywords: square-free number, exponential sum, exponent pair

Résumé - Abstract

It is proved that the sequence $[n^c] (n = 1, 2, \cdots )$ contains infinite squarefree integers whenever $1 < c < \frac{61}{36} = 1.6944 \cdots $, which improves Rieger’s earlier range $1 < c < 1.5$.

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