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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Correlations of multiplicative functions along deterministic and independent sequences


Author: Nikos Frantzikinakis
Journal: Trans. Amer. Math. Soc. 373 (2020), 6595-6620
MSC (2010): Primary 11N37, 37A45; Secondary 11K65
DOI: https://doi.org/10.1090/tran/8142
Published electronically: July 8, 2020
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Abstract: We study correlations of multiplicative functions taken along deterministic sequences and sequences that satisfy certain linear independence assumptions. The results obtained extend recent results of Tao and Teräväinen and results of the author. Our approach is to use tools from ergodic theory in order to effectively exploit feedback from analytic number theory. The results on deterministic sequences crucially use structural properties of measure preserving systems associated with bounded multiplicative functions that were recently obtained by the author and Host. The results on independent sequences depend on multiple ergodic theorems obtained using the theory of characteristic factors and qualitative equidistribution results on nilmanifolds.


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Additional Information

Nikos Frantzikinakis
Affiliation: Department of Mathematics and Applied Mathematics, University of Crete, Voutes University Campus, Heraklion 71003, Greece
MR Author ID: 712393
Email: frantzikinakis@gmail.com

DOI: https://doi.org/10.1090/tran/8142
Keywords: Multiplicative functions, Liouville function, Chowla conjecture, Elliott conjecture, Furstenberg correspondence
Received by editor(s): October 29, 2019
Received by editor(s) in revised form: February 6, 2020
Published electronically: July 8, 2020
Additional Notes: The author was supported by the Hellenic Foundation for Research and Innovation, Project No. 1684.
Article copyright: © Copyright 2020 American Mathematical Society