Equivalent definitions of oscillating sequences of higher orders

2017/05/22 by Ruxi Shi, Shi, Ruxi
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Coding theory and cryptography #Dynamical Systems (math.DS) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1705.07827

openalex publication_date 2017/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An oscillating sequence of order d is defined by the linearly disjointness from all \e^{2πi P(n)} \_n=1^∞ 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.

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