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

El Houcein El Abdalaoui; Joanna Kułaga-Przymus; Mariusz Lemańczyk; Thierry de la Rue

doi:10.3934/dcds.2017125

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2017, Volume 37, Issue 6: 2899-2944. Doi: 10.3934/dcds.2017125

This issue Previous Article Next Article Singular cw-expansive flows

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

1.
Laboratoire de Mathématiques Raphaël Salem, Normandie Université, Université de Rouen, CNRS, Avenue de l'Université, 76801 Saint Etienne du Rouvray, France
2.
Institute of Mathematics, Polish Acadamy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland, and, Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
3.
Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
4.
Laboratoire de Mathématiques Raphaël Salem, Normandie Université, Université de Rouen, CNRS, Avenue de l'Université, 76801 Saint Etienne du Rouvray, France

Received: March 31, 2015

Revised: December 31, 2016

Published: May 2017

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Abstract

We rephrase the conditions from the Chowla and the Sarnak conjectures in abstract setting, that is, for sequences in $\{-1,0,1\}^{{\mathbb{N}^*}}$, 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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Mathematics Subject Classification: Primary: 37A45, 37B10; Secondary: 11N37.

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