Sequences with bounded logarithmic discrepancy
Published online by Cambridge University Press: 24 October 2008
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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