Sarnak's conjecture implies the Chowla conjecture along a subsequence
Number Theory
2017-10-20 v1 Dynamical Systems
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.
Cite
@article{arxiv.1710.07049,
title = {Sarnak's conjecture implies the Chowla conjecture along a subsequence},
author = {Alexander Gomilko and Dominik Kwietniak and Mariusz Lemańczyk},
journal= {arXiv preprint arXiv:1710.07049},
year = {2017}
}
Comments
Proceedings of the Chair Morlet semester "Ergodic Theory and Dynamical Systems in their Interactions with Arithmetic and Combinatorics" 1.08.2016--31.01.2017, Springer, to appear