Geodesic
The Distribution of Sequences Modulo 1
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 697-709

Voir la notice de l'article provenant de la source Cambridge University Press

In a recent paper (2), Helson and Kahane consider the problem of the existence of real numbers x such that the sequence (λn x) (when reduced modulo 1) is not summable by a given regular Toeplitz method, where (λn) is a lacunary sequence of positive real numbers. Thus, as an example, they show the existence of uncountably many x such that the sequence (θn x) does not have a distribution function modulo 1, where θ is some fixed number > 1. 
Zame, Alan. The Distribution of Sequences Modulo 1. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 697-709. doi: 10.4153/CJM-1967-064-0
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