On the Erdős-Turán inequality for balls

Glyn Harman

Acta Arithmetica (1998)

  • Volume: 85, Issue: 4, page 389-396
  • ISSN: 0065-1036

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Glyn Harman. "On the Erdős-Turán inequality for balls." Acta Arithmetica 85.4 (1998): 389-396. <http://eudml.org/doc/207176>.

@article{GlynHarman1998,
author = {Glyn Harman},
journal = {Acta Arithmetica},
keywords = {Erdős-Turán inequality; ball discrepancy; torus},
language = {eng},
number = {4},
pages = {389-396},
title = {On the Erdős-Turán inequality for balls},
url = {http://eudml.org/doc/207176},
volume = {85},
year = {1998},
}

TY - JOUR
AU - Glyn Harman
TI - On the Erdős-Turán inequality for balls
JO - Acta Arithmetica
PY - 1998
VL - 85
IS - 4
SP - 389
EP - 396
LA - eng
KW - Erdős-Turán inequality; ball discrepancy; torus
UR - http://eudml.org/doc/207176
ER -

References

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  1. [1] R. C. Baker, Diophantine Inequalities, Oxford Univ. Press, 1986. Zbl0592.10029
  2. [2] J. Beck and W. W. L. Chen, Irregularities of Distribution, Cambridge Univ. 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] G. Harman, Small fractional parts of additive forms, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 339-347. Zbl0792.11018
  6. [6] G. Harman, Metric Number Theory, Oxford Univ. Press, 1998. Zbl1081.11057
  7. [7] J. J. Holt, On a form of the Erdős-Turán inequality, Acta Arith. 74 (1996), 61-66. Zbl0851.11042
  8. [8] J. J. Holt and J. D. Vaaler, The Beurling-Selberg extremal functions for a ball in Euclidean space, Duke Math. J. 83 (1996), 203-248. Zbl0859.30029
  9. [9] J. F. Koksma, Some theorems on Diophantine inequalities, Math. Centrum Amsterdam Scriptum no. 5. 
  10. [10] H. L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Amer. Math. Soc., Providence, R.I., 1994. Zbl0814.11001
  11. [11] W. M. Schmidt, Metrical theorems on fractional parts of sequences, Trans. Amer. Math. Soc. 110 (1964), 493-518. Zbl0199.09402
  12. [12] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J., 1971. Zbl0232.42007
  13. [13] P. Szüsz, Über ein Problem der Gleichverteilung, in: Comptes Rendus du Premier Congrès des Mathématiciens Hongrois, 1950, 461-472. 
  14. [14] S. K. Zaremba, Good lattice points in the sense of Hlawka and Monte Carlo integration, Monatsh. Math. 72 (1968), 264-269. Zbl0195.19501

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