, Volume 96, Issue 3, pp 173-181

Homogeneously distributed sequences and Poincaré sequences of integers of sublacunary growth

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The sequence of integersn 1<n 2<n 3<... is said to be homogeneously distributed if \(\mathop {\lim }\limits_{m \to + \infty } (1/m)\sum\limits_{k = 1}^m {\exp (2\pi in_k \alpha )} = 0\) for all non-integral real α. The existence of such sequences with a prescribed subexponential growth is shown, the recurrent properties of these sequences are discussed.