Correlations of multiplicative functions along deterministic and independent sequences
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- by Nikos Frantzikinakis PDF
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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.References
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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
- ORCID: 0000-0001-7392-5387
- Email: frantzikinakis@gmail.com
- 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.
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 6595-6620
- MSC (2010): Primary 11N37, 37A45; Secondary 11K65
- DOI: https://doi.org/10.1090/tran/8142
- MathSciNet review: 4155186