Construction of some Chowla sequences
Ruxi Shi

TL;DR
This paper introduces the Chowla property for numerical sequences, proves its implications, and demonstrates that almost all exponential sequences with base greater than one possess this property, linking it to orthogonality in dynamical systems.
Contribution
It establishes the Chowla property for certain sequences, proves it implies the Sarnak property, and constructs dependent random sequences with almost sure Chowla property.
Findings
Almost every exponential sequence with base > 1 has Chowla property.
Chowla property implies Sarnak property.
Dependent random sequences can have almost sure Chowla property.
Abstract
For numerical sequences taking values or complex numbers of modulus , we define Chowla property and Sarnak property. We prove that Chowla property implies Sarnak property. We also prove that for Lebesgue almost every , the sequence 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Analytic Number Theory Research · Benford’s Law and Fraud Detection
