Construction of some Chowla sequences

Ruxi Shi

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arXiv · 1804.03851

Construction of some Chowla sequences

Ruxi Shi

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Abstract

For numerical sequences taking values $0$ or complex numbers of modulus $1$, we define Chowla property and Sarnak property. We prove that Chowla property implies Sarnak property. We also prove that for Lebesgue almost every $β>1$, the sequence $(e^{2πβ^n})_{n\in \mathbb{N}}$ shares Chowla property and consequently is orthogonal to all topological dynamical systems of zero entropy. It is also discussed whether the samples of a given random sequence have Chowla property almost surely. Some dependent random sequences having almost surely Chowla property are constructed.

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BibTeX RIS

Ruxi Shi. 2018-04-24. Construction of some Chowla sequences. https://arxiv.org/abs/1804.03851

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