Abstract
We show that the Möbius disjointess of zero entropy dynamical systems implies the existence of an increasing sequence of positive integers along which the Chowla conjecture on autocorrelations of the Möbius function holds.
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Acknowledgements
The research of the first author was supported by Narodowe Centrum Nauki grant 2014/13/B/ST1/03153. The research of the second author was supported by Narodowe Centrum Nauki grant UMO-2012/07/E/ST1/00185. The research of the third author was supported by Narodowe Centrum Nauki grant UMO-2014/15/B/ST1/03736.
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Gomilko, A., Kwietniak, D., Lemańczyk, M. (2018). Sarnak’s Conjecture Implies the Chowla Conjecture Along a Subsequence. In: Ferenczi, S., Kułaga-Przymus, J., Lemańczyk, M. (eds) Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics. Lecture Notes in Mathematics, vol 2213. Springer, Cham. https://doi.org/10.1007/978-3-319-74908-2_12
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