Correlations of multiplicative functions along deterministic and independent sequences

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 or...

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Veröffentlicht in:Transactions of the American Mathematical Society 2020-09, Vol.373 (9), p.6595-6620
1. Verfasser: Frantzikinakis, Nikos
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/8142