# Odd order cases of the logarithmically averaged Chowla conjecture

@article{Tao2017OddOC,
title={Odd order cases of the logarithmically averaged Chowla conjecture},
author={Terence Tao and Joni Teravainen},
journal={Journal de Theorie des Nombres de Bordeaux},
year={2017},
volume={30},
pages={997-1015}
}
• Published 5 October 2017
• Mathematics
• Journal de Theorie des Nombres de Bordeaux
A famous conjecture of Chowla states that the Liouville function $\lambda(n)$ has negligible correlations with its shifts. Recently, the authors established a weak form of the logarithmically averaged Elliott conjecture on correlations of multiplicative functions, which in turn implied all the odd order cases of the logarithmically averaged Chowla conjecture. In this note, we give a new and shorter proof of the odd order cases of the logarithmically averaged Chowla conjecture. In particular…
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