On a form of the Erdős-Turán inequality
Jeffrey J. Holt
Acta Arithmetica, Tome 76 (1996), p. 61-66 / Harvested from The Polish Digital Mathematics Library
Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:206837
@article{bwmeta1.element.bwnjournal-article-aav74i1p61bwm,
     author = {Jeffrey J. Holt},
     title = {On a form of the Erd\H os-Tur\'an inequality},
     journal = {Acta Arithmetica},
     volume = {76},
     year = {1996},
     pages = {61-66},
     zbl = {0851.11042},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav74i1p61bwm}
}
Jeffrey J. Holt. On a form of the Erdős-Turán inequality. Acta Arithmetica, Tome 76 (1996) pp. 61-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav74i1p61bwm/

[000] [1] R. C. Baker, Diophantine Inequalities, Oxford University Press, New York, 1986.

[001] [2] J. Beck and W. W. L. Chen, Irregularities of Distribution, Cambridge University Press, 1987. | Zbl 0617.10039

[002] [3] T. Cochrane, Trigonometric approximation and uniform distribution modulo 1, Proc. Amer. Math. Soc. 103 (1988), 695-702. | Zbl 0667.10031

[003] [4] P. Erdős and P. Turán, On a problem in the theory of uniform distribution, I, Indag. Math. 10 (1948), 370-378.

[004] [5] P. J. Grabner, Erdős-Turán type discrepancy bounds, Monatsh. Math. 111 (1991), 127-135. | Zbl 0719.11046

[005] [6] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford University Press, Oxford, 1979. | Zbl 0423.10001

[006] [7] J. J. Holt and J. D. Vaaler, The Beurling-Selberg extremal functions for a ball in Euclidean space, to appear. | Zbl 0859.30029

[007] [8] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974. | Zbl 0281.10001

[008] [9] W. M. Schmidt, Irregularities of distribution, IV, Invent. Math. 7 (1969), 55-82.

[009] [10] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, N.J., 1971. | Zbl 0232.42007

[010] [11] P. Szüsz, Über ein Problem der Gleichverteilung, in: Comptes Rendus du Premier Congrès des Mathématiciens Hongrois, 1950, 461-472.

[011] [12] J. D. Vaaler, Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc. 12 (1985), 183-216. | Zbl 0575.42003

[012] [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 | Zbl 0787.11031