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Notes on Erdös-Turán inequality

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  09 April 2009

Yukio Ohkubo
Yukio Ohkubo
Affiliation:
Faculty of Economics Kagoshima Keizai University Shimofukumoto-cho Kagoshima-shi 891-0191 Japan e-mail: [email protected]
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Abstract

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A new version of Erdös-Turán's inequality is described. The purpose of the present paper is to show that the inequality provides better upper bounds for the discrepancies of some sequences than usual Erdös-Turán's inequality.

Keywords

DiscrepancyErdös-Turán's inequalityexponential sumvan der Corput's method.

MSC classification

Secondary: 11K38: Irregularities of distribution, discrepancy
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 67 , Issue 1 , August 1999 , pp. 51 - 57
Copyright
Copyright © Australian Mathematical Society 1999

References

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