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Sequences with bounded logarithmic discrepancy

Published online by Cambridge University Press:  24 October 2008

R. C. Baker  and
G. Harman
R. C. Baker
Affiliation:
Department of Mathematics, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX
G. Harman
Affiliation:
School of Mathematics, University of Wales College of Cardiff, Senghenydd Road, Cardiff CF2 4AG
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Extract

Let {α} denote the fractional part of the real number α. Write χ(x, y) = 1 for {x} < y and χ(x, y) = 0 otherwise. A real sequence (xn) is uniformly distributed (mod 1) if

It is a consequence of (1·1) that DN = o(N),

Where

is the discrepancy of the sequence (xn).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 2 , March 1990 , pp. 213 - 225
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

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