Mathematical analysis/Dynamical systems
Fully oscillating sequences and weighted multiple ergodic limit
Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 866-870.

We prove that fully oscillating sequences are orthogonal to multiple ergodic realizations of affine maps of zero entropy on compact Abelian groups. It is more than what Sarnak's conjecture requires for these dynamical systems.

Nous montrons que les suites pleinement oscillantes sont orthogonales aux réalisations d'une application affine d'entropie nulle sur un groupe abélien compact. Ceci est plus que ce que demande la conjecture de Sarnak à ces systèmes dynamiques.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.07.008
Fan, Aihua 1, 2

1 LAMFA, UMR 7352 CNRS, Université de Picardie, 33, rue Saint-Leu, 80039 Amiens, France
2 School of Mathematics and Statistics, Huazhong Normal University, Wuhan 430079, China
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Fan, Aihua. Fully oscillating sequences and weighted multiple ergodic limit. Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 866-870. doi : 10.1016/j.crma.2017.07.008. http://www.numdam.org/articles/10.1016/j.crma.2017.07.008/

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