Oscillating sequences of higher orders and topological systems of quasi-discrete spectrum

Abstract

Fully oscillating sequences are orthogonal to all topological dynamical systems of quasi-discrete spectrum in the sense of Hahn-Parry. This orthogonality concerns with not only simple but also multiple ergodic means. It is stronger than that required by Sarnak's conjecture.

7 pages

References in corpus (1)

• Möbius disjointness for topological models of ergodic systems with discrete spectrum

Cited by in corpus (5)

• Topological Wiener-Wintner ergodic theorem with polynomial weights
• On uniformity of $q$-multiplicative sequences
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• Weighted Birkhoff ergodic theorem with oscillating weights
• A rigorous computer aided estimation for Gelfond exponent of weighted Thue-Morse sequences