On a form of the Erdős-Turán inequality

Jeffrey J. Holt

Acta Arithmetica (1996)

  • Volume: 74, Issue: 1, page 61-66
  • ISSN: 0065-1036

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Jeffrey J. Holt. "On a form of the Erdős-Turán inequality." Acta Arithmetica 74.1 (1996): 61-66. <http://eudml.org/doc/206837>.

@article{JeffreyJ1996,
author = {Jeffrey J. Holt},
journal = {Acta Arithmetica},
keywords = {Erdös-Turan inequality; discrepancy},
language = {eng},
number = {1},
pages = {61-66},
title = {On a form of the Erdős-Turán inequality},
url = {http://eudml.org/doc/206837},
volume = {74},
year = {1996},
}

TY - JOUR
AU - Jeffrey J. Holt
TI - On a form of the Erdős-Turán inequality
JO - Acta Arithmetica
PY - 1996
VL - 74
IS - 1
SP - 61
EP - 66
LA - eng
KW - Erdös-Turan inequality; discrepancy
UR - http://eudml.org/doc/206837
ER -

References

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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

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