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Discrepancy of the sequence $$\Big(\Big\{n{1+\sqrt{5}\over 2}\Big\}\Big)$$. (Discrépance de la suite $$\Big(\Big\{n{1+\sqrt{5}\over 2}\Big\}\Big)$$.) (French) Zbl 0386.10021
Let $$D^*(N)$$ be the star-discrepancy of the sequence $$\Big(\Big\{n{1+\sqrt{5}\over 2}\Big\}\Big)$$. We show that
$\limsup {D^*(N)\over \log N} = {3\over 20} \Big(\log{1+\sqrt 5\over 2}\Big) ^{-1} = 0.31\cdots,$ which illustrates the fact that our sequence has smaller star-discrepancy than that of van der Corput’s sequence. Our proofs involve continued fraction theory.
Reviewer: Yves Dupain

##### MSC:
 11K06 General theory of distribution modulo $$1$$ 11K31 Special sequences
##### Keywords:
star discrepancy; uniform distribution
Full Text:
##### References:
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