The Chowla and the Sarnak conjectures from ergodic theory point of view

By el Houcein el Abdalaoui, J. Kułaga-Przymus, Mariusz Lemanczyk, Thierry de la Rue. 2014

91 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a182cb17ade9f6fd239c55a22d0649cac7e01cae

Citations in the corpus

• Automorphisms with quasi-discrete spectrum, multiplicative functions and average orthogonality along short intervals (2015, unknown): “Sarnak’s conjecture has been proved to hold in several cases [1–3,6–9, 11 So far, the only automorphisms for which Sarnak’s conjecture was known to hold in each of their uniquely ergodic model were those whose prime powers are disjoint in the sense of Furstenberg [12].”