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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 proof of the odd order cases of the logarithmically averaged Chowla conjecture. In particular, this proof ...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.5802/jtnb.1062

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
Publisher:
Société Arithmétique de Bordeaux Publisher's website
Journal:
Journal de théorie des nombres de Bordeaux Journal website
Volume:
30
Issue:
3
Pages:
997-1015
Publication date:
2019-04-19
Acceptance date:
2018-04-10
DOI:
EISSN:
2118-8572
ISSN:
1246-7405
Pubs id:
pubs:935443
URN:
uri:01a2f7c5-4a7a-4d39-ad6b-9a9a13f05485
UUID:
uuid:01a2f7c5-4a7a-4d39-ad6b-9a9a13f05485
Local pid:
pubs:935443

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