2019/08/07 by Nikos Frantzikinakis, Frantzikinakis, Nikos
Mathematics · #11K65 (Secondary) #11N37 (Primary) #37A45 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1908.02732
openalex publication_date 2019/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study correlations of multiplicative functions taken along deterministic\nsequences and sequences that satisfy certain linear independence assumptions.\nThe results obtained extend recent results of Tao and Ter "av "ainen and\nresults of the author. Our approach is to use tools from ergodic theory in\norder to effectively exploit feedback from analytic number theory. The results\non deterministic sequences crucially use structural properties of measure\npreserving systems associated with bounded multiplicative functions that were\nrecently obtained by the author and Host. The results on independent sequences\ndepend on multiple ergodic theorems obtained using the theory of characteristic\nfactors and qualitative equidistribution results on nilmanifolds.\n