Monatshefte für Mathematik

, Volume 96, Issue 3, pp 173–181

Homogeneously distributed sequences and Poincaré sequences of integers of sublacunary growth

  • Michael Boshernitzan

DOI: 10.1007/BF01605486

Cite this article as:
Boshernitzan, M. Monatshefte für Mathematik (1983) 96: 173. doi:10.1007/BF01605486


The sequence of integersn1<n2<n3<... 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.

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Michael Boshernitzan
    • 1
  1. 1.Department of MathematicsRice UniversityHoustonUSA