Abstract
We use the notion of self-similar sequences, introduced by the author in [1], to obtain in a natural way some sequences of points in the interval [0, 1] with the property:
whereL(U) and ℓ (U) stand respectively for the lim sup and the lim inf of the ratioN·D *N (U)/LogN. HereD *N (U) is the star discrepancy of the sequenceU.
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Cet article a été rédigé lors d'un séjour de recherche de l'auteur à l'Université de Provence, à Marseille.
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Borel, JP. Suites dont la discrépance est comparable à un logarithme. Monatshefte für Mathematik 110, 207–216 (1990). https://doi.org/10.1007/BF01301676
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DOI: https://doi.org/10.1007/BF01301676