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The discrepancy of the sequence \((n\alpha + (\log n)\beta)\). (English) Zbl 0980.11032

Summary: We give an upper bound for the discrepancy of the sequence \((n\alpha+(\log n)\beta)\), where \(\alpha=(\alpha_1,\dots,\alpha_s)\in \mathbb{R}^s\), which satisfies the conditions that \(1,\alpha_1,\dots,\alpha_s\) are linearly independent over \(\mathbb{Z}\), is of finite type \(\eta\) or is of constant type.

MSC:

11K38 Irregularities of distribution, discrepancy
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