[Suites pleinement oscillantes et limite des moyennes multi-ergodiques pondérées]
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.
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.
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@article{CRMATH_2017__355_8_866_0,
author = {Aihua Fan},
title = {Fully oscillating sequences and weighted multiple ergodic limit},
journal = {Comptes Rendus. Math\'ematique},
pages = {866--870},
publisher = {Elsevier},
volume = {355},
number = {8},
year = {2017},
doi = {10.1016/j.crma.2017.07.008},
language = {en},
}
Aihua Fan. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.07.008/
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