The integral mean of the discrepancy of the sequence \((n\alpha)\) (Q1596341)
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scientific article; zbMATH DE number 1562963
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The integral mean of the discrepancy of the sequence \((n\alpha)\) |
scientific article; zbMATH DE number 1562963 |
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The integral mean of the discrepancy of the sequence \((n\alpha)\) (English)
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22 November 2001
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Let \(D_N(\alpha)\) be the discrepancy of the sequence \((n\alpha)_{n=1}^N\) modulo 1, where \(\alpha\) is a given real number. Then it is proved that \[ \lim_{N\to\infty} \frac{1} {\log^2 N} \int_0^1 D_N(\alpha) d\alpha= \frac{1}{\pi^2}. \]
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discrepancy
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