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On the discrepancy of the sequence formed from multiples of an irrational number

Published online by Cambridge University Press:  17 April 2009

Tony van Ravenstein
Tony van Ravenstein
Affiliation:
Department of Mathematics, University of Wollongong, Wollongon, New South Wales 2500, Australia.
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Abstract

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This paper demonstrates a connection between two measures of discrepancy of sequences which arise in the theory of uniform distribution modulo one. The sequence formed from the non-negative integer multiples of an irrational number ξ is investigated and, by an application of the “Steinhaus Conjecture”, some values of the two discrepancies are obtained using continued fractions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 31 , Issue 3 , June 1985 , pp. 329 - 338
Copyright
Copyright © Australian Mathematical Society 1985

References

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