Collectanea Mathematica

, Volume 69, Issue 3, pp 395–405 | Cite as

Equivalent definitions of oscillating sequences of higher orders

  • Ruxi ShiEmail author


An oscillating sequence of order d is defined by the linearly disjointness from all \(\{e^{2\pi i P(n)} \}_{n=1}^{\infty }\) for all real polynomials P of degree smaller or equal to d. A fully oscillating sequence is defined to be an oscillating sequence of all orders. In this paper, we give several equivalent definitions of such sequences in terms of their disjointness from different dynamical systems on tori.


Oscillating sequence Linearly disjoint Affine map on tori Quasi-unipotent 

Mathematics Subject Classification

11N37 37A45 



The authors are grateful to the anonymous reviewer for their valuable remarks.


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Copyright information

© Universitat de Barcelona 2017

Authors and Affiliations

  1. 1.LAMFA, UMR 7352 CNRSUniversité de PicardieAmiensFrance

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