Shi, R. Construction of some Chowla sequences. Monatsh Math 194, 193–224 (2021). https://doi.org/10.1007/s00605-020-01448-x

### Construction of some Chowla sequences

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Author: Shi, Ruxi1
Organizations: 1Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, 90014, Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.5 MB)
Language: English
Published: Springer Nature, 2021
Publish Date: 2021-05-19
Description:

# Abstarct

In this paper, we show that for a twice differentiable function $$g$$ having countable zeros and for Lebesgue almost every $$\beta > 1$$, the sequence $$(e^{2\pi i \beta ^ng(\beta )})_{n\in {\mathbb {N}}}$$ is orthogonal to all topological dynamical systems of zero entropy. To this end, we define the Chowla property and the Sarnak property for numerical sequences taking values 0 or complex numbers of modulus 1. We prove that the Chowla property implies the Sarnak property and show that for Lebesgue almost every $$\beta > 1$$, the sequence $$(e^{2\pi i \beta ^n})_{n\in {\mathbb {N}}}$$ shares the Chowla property. It is also discussed whether the samples of a given random sequence have the Chowla property almost surely. Some dependent random sequences having almost surely the Chowla property are constructed.

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Series: Monatshefte für Mathematik
ISSN: 0026-9255
ISSN-E: 1436-5081
ISSN-L: 0026-9255
Volume: 194
Issue: 1
Pages: 193 - 224
DOI: 10.1007/s00605-020-01448-x