On the sum of the fractional parts \(\sum_{n\leq x}\{ne\}\) (Q2857779)
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scientific article; zbMATH DE number 6228988
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the sum of the fractional parts \(\sum_{n\leq x}\{ne\}\) |
scientific article; zbMATH DE number 6228988 |
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19 November 2013
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fractional parts
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continued fraction for \(e\)
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0.93002146
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0.8872597
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0.88454825
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0.8789636
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0.8765498
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On the sum of the fractional parts \(\sum_{n\leq x}\{ne\}\) (English)
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Let \(C(x):=\sum_{n \leq x} (\{n e\}-1/2)\). The author shows that \(C(x)=O((\log x/\log \log x)^2)\) and that this bound is sharp. The proof is based on an earlier paper of \textit{T. C. Brown} and \textit{P. J. S. Shiue} [J. Number Theory 50, No. 2, 181--192 (1995; Zbl 0824.11041)].
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