On a form of the Erdős-Turán inequality

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1. [1] R. C. Baker, Diophantine Inequalities, Oxford University Press, New York, 1986. 
2. [2] J. Beck and W. W. L. Chen, Irregularities of Distribution, Cambridge University Press, 1987. Zbl0617.10039
3. [3] T. Cochrane, Trigonometric approximation and uniform distribution modulo 1, Proc. Amer. Math. Soc. 103 (1988), 695-702. Zbl0667.10031
4. [4] P. Erdős and P. Turán, On a problem in the theory of uniform distribution, I, Indag. Math. 10 (1948), 370-378. 
5. [5] P. J. Grabner, Erdős-Turán type discrepancy bounds, Monatsh. Math. 111 (1991), 127-135. Zbl0719.11046
6. [6] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford University Press, Oxford, 1979. Zbl0423.10001
7. [7] J. J. Holt and J. D. Vaaler, The Beurling-Selberg extremal functions for a ball in Euclidean space, to appear. Zbl0859.30029
8. [8] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974. Zbl0281.10001
9. [9] W. M. Schmidt, Irregularities of distribution, IV, Invent. Math. 7 (1969), 55-82. 
10. [10] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, N.J., 1971. Zbl0232.42007
11. [11] P. Szüsz, Über ein Problem der Gleichverteilung, in: Comptes Rendus du Premier Congrès des Mathématiciens Hongrois, 1950, 461-472. 
12. [12] J. D. Vaaler, Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc. 12 (1985), 183-216. Zbl0575.42003
13. [13] J. D. Vaaler, Refinements of the Erdős-Turán inequality, in: Number Theory with an Emphasis on the Markoff Spectrum, W. Moran and A. Pollington (eds.), Marcel Dekker, New York, 1993, 263-269 Zbl0787.11031

1. Glyn Harman, On the Erdős-Turán inequality for balls