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A metrical result on the discrepancy of (nα)

Published online by Cambridge University Press:  18 May 2009

J. Schoissengeier
J. Schoissengeier
Affiliation:
Institut für Mathematik, Universität Wien, Strudlhofgasse 4A-1090 Wien, Austria
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In the following let Ω be the set of irrational numbers in the interval [0,1] and let λ be Lebesgue measure restricted to Ω. For any real number x, let {x} = x - [x] be the fractional part of x. Let N be anatural number and let α e Ω. Then

is known as the discrepancy of the sequence (nα)n>1 modulo 1; here c[x, y) denotes the characteristic function of the interval [x, y).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 3 , September 1998 , pp. 393 - 425
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

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