The Chowla and the Sarnak conjectures from ergodic theory point of view
El Houcein El Abdalaoui (LMRS), Joanna Kulaga-Przymus, Mariusz, Lemanczyk, Thierry De La Rue (LMRS)
TL;DR
This paper explores the Chowla and Sarnak conjectures within ergodic theory, reformulating their conditions for sequences in {-1,0,1} and examining their connections to topological dynamics.
Contribution
It introduces a generalized framework for the conjectures and investigates their relationships with concepts in ergodic theory and topological dynamics.
Findings
Reformulation of Chowla and Sarnak conditions in an abstract setting
Identification of relationships with topological dynamics
Introduction of natural generalizations of the conjectures
Abstract
We rephrase the conditions from the Chowla and the Sarnak conjectures in abstract setting, that is, for sequences of numbers in {-1,0,1}, and introduce several natural generalizations. We study the relationships between these properties and other notions from topological dynamics and ergodic theory.
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Taxonomy
TopicsAnalytic Number Theory Research · Benford’s Law and Fraud Detection · Mathematical Dynamics and Fractals