Sarnak's conjecture implies the Chowla conjecture along a subsequence

Alexander Gomilko; Dominik Kwietniak; Mariusz Lemańczyk

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arXiv · 1710.07049

Sarnak's conjecture implies the Chowla conjecture along a subsequence

Alexander Gomilko·Dominik Kwietniak·Mariusz Lemańczyk

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Abstract

We show that the M\"obius 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 M\"obius function holds.

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Alexander Gomilko, Dominik Kwietniak, Mariusz Lemańczyk. 2017-10-19. Sarnak's conjecture implies the Chowla conjecture along a subsequence. https://arxiv.org/abs/1710.07049

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