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

El Houcein El Abdalaoui (1) , Joanna Kulaga-Przymus (2) , Mariusz Lemanczyk (2) , Thierry de La Rue (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 Faculty of Mathematics and Computer Science

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.

Mots clés: Möbius function; Sarnak conjecture; Chowla conjecture; entropy

Domaines: Systèmes dynamiques [math.DS]; Théorie des nombres [math.NT]

El Houcein El Abdalaoui, Joanna Kulaga-Przymus, Mariusz Lemanczyk, Thierry de La Rue. The Chowla and the Sarnak conjectures from ergodic theory point of view. 2014. ⟨hal-01070531v1⟩