Odd order cases of the logarithmically averaged Chowla conjecture

Abstract

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, this proof avoids all mention of ergodic theory, which had an important role in the previous proof.

15 pages, no figures, submitted, J. Numb. Thy. Bordeaux

References in corpus (2)

• The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures
• Nilsequences and Multiple Correlations along Subsequences

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• The Hardy--Littlewood--Chowla conjecture in the presence of a Siegel zero
• Value patterns of multiplicative functions and related sequences
• Gowers norms control diophantine inequalities
• The Chowla conjecture and Landau-Siegel zeroes
• Random Chowla's Conjecture for Rademacher Multiplicative Functions
• On variants of Chowla's conjecture