A polynomial version of Sarnak's conjecture

DOI10.1016/j.crma.2015.04.009zbMath1316.37008arXiv1501.04323OpenAlexW2963666230WikidataQ123344244 ScholiaQ123344244MaRDI QIDQ2352214

Tetyana Lobova

Publication date: 30 June 2015

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.04323

zbMATH Keywords

Möbius functionminimal systemsSarnak conjecture

Mathematics Subject Classification ID

Related Items (7)

Möbius orthogonality of sequences with maximal entropy ⋮ Automatic sequences as good weights for ergodic theorems ⋮ Equivalence of the Logarithmically Averaged Chowla and Sarnak Conjectures ⋮ On the rate of convergence of weighted oscillating ergodic averages ⋮ Topological Wiener-Wintner ergodic theorem with polynomial weights ⋮ Disjointness of the Möbius transformation and Möbius function ⋮ Weighted Birkhoff ergodic theorem with oscillating weights

Cites Work

• The quantitative behaviour of polynomial orbits on nilmanifolds
• The Möbius function is strongly orthogonal to nilsequences
• The Chowla and the Sarnak conjectures from ergodic theory point of view
• Ergodic theorems with arithmetical weights
• Pointwise ergodic theorems for arithmetic sets. With an appendix on return-time sequences, jointly with Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein
• Quadratic uniformity of the Möbius function
• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Complexity of nilsystems and systems lacking nilfactors
• Convergence of weighted polynomial multiple ergodic averages
• Topological Sequence Entropy
• Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold
• Disjointness of Moebius from Horocycle Flows
• Multiple ergodic theorems for arithmetic sets
• Polynomial extensions of van der Waerden’s and Szemerédi’s theorems

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