Lower bounds for the discrepancy of some sequences

Kazuo Goto; Yukio Ohkubo

Mathematica Slovaca (2004)

  • Volume: 54, Issue: 5, page 487-502
  • ISSN: 0232-0525

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Goto, Kazuo, and Ohkubo, Yukio. "Lower bounds for the discrepancy of some sequences." Mathematica Slovaca 54.5 (2004): 487-502. <http://eudml.org/doc/32438>.

@article{Goto2004,
author = {Goto, Kazuo, Ohkubo, Yukio},
journal = {Mathematica Slovaca},
keywords = {uniformly distributed sequences; discrepancy; exponential sum},
language = {eng},
number = {5},
pages = {487-502},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Lower bounds for the discrepancy of some sequences},
url = {http://eudml.org/doc/32438},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Goto, Kazuo
AU - Ohkubo, Yukio
TI - Lower bounds for the discrepancy of some sequences
JO - Mathematica Slovaca
PY - 2004
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 54
IS - 5
SP - 487
EP - 502
LA - eng
KW - uniformly distributed sequences; discrepancy; exponential sum
UR - http://eudml.org/doc/32438
ER -

References

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  1. BINGHAM H.-GOLDIE, C M.-TEUGELS J. L., Regular Variation, Cambridge University Press, Cambridge, 1987. (1987) Zbl0617.26001MR0898871
  2. GOTO K.-OHKUBO Y., The discrepancy of the sequence ( n α + ( log n ) β ) , Acta Matһ. Hungar. 86 (2000), 39-47. Zbl0980.11032MR1728588
  3. GOТO K.-OHKUBO Y., Discrepancy of some special sequences, In: Analytic Number Тheory (C Jia, K. Matsumoto, eds.), Dev. Math. 6, Kluwer Academic Publishers, Dordrecht, 2002, pp. 143-155. MR1901979
  4. IVIĆ A., The Riemann Zeta-Function, Joһn Wiley and Sons, New York, 1985. (1985) Zbl0583.10021MR0792089
  5. KARAТSUBA A. A.-VORONIN S. M., The Riemann Zeta-Function, Walter de Gruyter, Berlin, 1992. (1992) MR1183467
  6. KUIPERS L.-NIEDERREIТER H., Uniform Distributгon of Sequences, Joһn Wiley and Sons, New York, 1974. (1974) MR0419394
  7. OHKUBO Y., Notes on Erdös-Turán inequality, J. Aust. Math. Sоc. Ser. A 67 (1999), 51-57. (1999) Zbl0940.11029MR1699155
  8. ТIТCHMARSH E. C., The Theory of the Riemann Zeta-Function, (2nd ed. revised by D. R. Heatһ-Brоwn), Clarendоn Press, Oxfоrd, 1986. (1986) MR0882550
  9. ZYGMUND A., Trigonometric Series Vol. I, Cambridge University Press, Cambridge, 1977. (1977) Zbl0367.42001MR0617944

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