A1 Refereed original research article in a scientific journal
Odd order cases of the logarithmically averaged chowla conjecture
Authors: Tao T., Teräväinen J.
Publisher: Institut de Mathematique de Bordeaux
Publication year: 2018
Journal: Journal De Theorie Des Nombres De Bordeaux
Journal name in source: Journal de Theorie des Nombres de Bordeaux
Volume: 30
Issue: 3
First page : 997
Last page: 1015
Number of pages: 19
ISSN: 1246-7405
DOI: https://doi.org/10.5802/jtnb.1062
Web address : http://jtnb.cedram.org/item?id=JTNB_2018__30_3_997_0
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/40610631
A famous conjecture of Chowla states that the Liouville function λ(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 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.
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