On the homogeneous ergodic bilinear averages with Möbius and Liouville weights

DOI10.1215/00192082-8165574zbMath1439.37006arXiv1706.07280OpenAlexW4300486147WikidataQ114060399 ScholiaQ114060399MaRDI QIDQ2305596

El Houcein El Abdalaoui

Publication date: 11 March 2020

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.07280

zbMATH Keywords

Möbius functionSarnak's conjectureLiouville functionmultilinear ergodic averagesPinsker algebra

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Asymptotic results on arithmetic functions (11N37) Ergodic theory of linear operators (47A35) Ergodic theorems, spectral theory, Markov operators (37A30) Arithmetic combinatorics; higher degree uniformity (11B30) Relations between ergodic theory and number theory (37A44)

Cites Work

• The Möbius function is strongly orthogonal to nilsequences
• The Chowla and the Sarnak conjectures from ergodic theory point of view
• Pointwise convergence of the ergodic bilinear Hilbert transform
• Mixing of all orders and pairwise independent joinings of systems with singular spectrum
• Multiple recurrence and almost sure convergence for weakly mixing dynamical systems
• Almost sure convergence of the multiple ergodic average for certain weakly mixing systems
• Extension of Wiener-Wintner double recurrence theorem to polynomials
• A non-singular dynamical system without maximal ergodic inequality
• Multiple return times theorems for weakly mixing systems
• Pointwise convergence of multiple ergodic averages and strictly ergodic models
• Pointwise characteristic factors for Wiener–Wintner double recurrence theorem
• Ergodic averages of commuting transformations with distinct degree polynomial iterates
• Maximal multilinear operators
• Convergence of weighted polynomial multiple ergodic averages
• Arithmetical Aspects of the Large Sieve Inequality
• An elementary proof of the strong law of large numbers
• On Multiplicative Arithmetical Functions whose Modulus does not Exceed One
• Double recurrence and almost sure convergence.
• Disjointness of Moebius from Horocycle Flows
• Some Special Trigonometrical Series Related To the Distribution of Prime Numbers
• Davenport's theorem in short intervals
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