A1 Refereed original research article in a scientific journal

Odd order cases of the logarithmically averaged chowla conjecture




AuthorsTao T., Teräväinen J.

PublisherInstitut de Mathematique de Bordeaux

Publication year2018

JournalJournal De Theorie Des Nombres De Bordeaux

Journal name in sourceJournal de Theorie des Nombres de Bordeaux

Volume30

Issue3

First page 997

Last page1015

Number of pages19

ISSN1246-7405

DOIhttps://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 addresshttps://research.utu.fi/converis/portal/detail/Publication/40610631


Abstract

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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