Notes on Erdős-Turán inequality. (English) Zbl 0940.11029

Following, R. C. Baker and G. Harman [Math. Proc. Camb. Philos. Soc. 107, 213-225 (1990; Zbl 0705.11040)] the author describes a new version of Erdős-Turán’s inequality. This new inequality can be used to obtain sharper discrepancy estimates for some special sequences. In particular, results of R. F. Tichy and G. Turnwald [Tsukuba J. Math. 10, 351-366 (1986; Zbl 0619.10031)] concerning the sequence \((n\alpha+ (\log n) \beta)_{n=1}^\infty\) are extended.
Reviewer: R.F.Tichy (Graz)


11K38 Irregularities of distribution, discrepancy
11J71 Distribution modulo one
11L03 Trigonometric and exponential sums (general theory)
11K31 Special sequences