Sarnak's conjecture implies the Chowla conjecture along a subsequence

Alexander Gomilko; Dominik Kwietniak; Mariusz Lema\'nczyk

arxiv: 1710.07049 · v1 · pith:2YTZDWTSnew · submitted 2017-10-19 · 🧮 math.NT · math.DS

Sarnak's conjecture implies the Chowla conjecture along a subsequence

Alexander Gomilko , Dominik Kwietniak , Mariusz Lema\'nczyk This is my paper

classification 🧮 math.NT math.DS

keywords conjecturealongchowlaimpliesobiusautocorrelationsdisjointessdynamical

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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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Sarnak's conjecture implies the Chowla conjecture along a subsequence

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