Automatic sequences are orthogonal to aperiodic multiplicative functions

DOI10.1007/978-3-030-62497-2_50zbMath1484.37008arXiv1811.00594OpenAlexW2898819295MaRDI QIDQ5918414

Mariusz Lemanczyk, Clemens Müllner

Publication date: 10 December 2021

Published in: Discrete and Continuous Dynamical Systems, 2019-20 MATRIX Annals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.00594

zbMATH Keywords

multiplicative functionsautomatic sequencessymbolic dynamical systemsautomatic sequenceodometerSarnak conjectureDKBSZ criterion

Mathematics Subject Classification ID

Formal languages and automata (68Q45) Asymptotic results on arithmetic functions (11N37) Ergodic theorems, spectral theory, Markov operators (37A30) Dynamical aspects of cellular automata (37B15) Arithmetic functions; related numbers; inversion formulas (11A25) Automata sequences (11B85) Relations between ergodic theory and number theory (37A44)

Related Items (6)

Torsion-free $S$-adic shifts and their spectrum ⋮ Monochromatic arithmetic progressions in automatic sequences with group structure ⋮ Automorphisms of automatic shifts ⋮ Automatic sequences are orthogonal to aperiodic multiplicative functions ⋮ Multiplicative automatic sequences ⋮ (Logarithmic) densities for automatic sequences along primes and squares

Cites Work

• Unnamed Item
• Unnamed Item
• Multiplicative functions in short intervals
• Spectral multiplicities for ergodic flows
• Substitutions in dynamics, arithmetics and combinatorics
• Möbius orthogonality for \(q\)-semimultiplicative sequences
• Prime numbers along Rudin-Shapiro sequences
• The Möbius function and continuous extensions of rotations
• An averaged form of Chowla's conjecture
• Substitution dynamical systems. Spectral analysis
• On a problem of Gelfond: the sum of digits of prime numbers
• A remark on a theorem of H. Daboussi
• Topological mixing and uniquely ergodic systems
• A criterion for a process to be prime
• Multiplicative functions and \(k\)-automatic sequences
• Möbius disjointness for models of an ergodic system and beyond
• Automatic sequences fulfill the Sarnak conjecture
• Sarnak's conjecture: what's new
• Sarnak's conjecture implies the Chowla conjecture along a subsequence
• The logarithmic Sarnak conjecture for ergodic weights
• Mock characters and the Kronecker symbol
• Automatic sequences generated by synchronizing automata fulfill the Sarnak conjecture
• Higher order Fourier analysis of multiplicative functions and applications
• Substitutions and Möbius disjointness
• Completely Multiplicative Automatic Functions
• Furstenberg Systems of Bounded Multiplicative Functions and Applications
• Subsequences of automatic sequences and uniform distribution
• Homomorphismes entre systèmes dynamiques définis par substitutions
• The spectrum of dynamical systems arising from substitutions of constant length
• Ergodic properties of group extensions of dynamical systems with discrete spectra
• Automatic Sequences
• Equivalence of the Logarithmically Averaged Chowla and Sarnak Conjectures
• Invariant sub-σ-algebras for substitutions of constant length
• Disjointness of Moebius from Horocycle Flows
• A Structure Theorem for Level Sets of Multiplicative Functions and Applications
• On multiplicative automatic sequences
• A note on multiplicative automatic sequences, II
• Compact subgroups in the centralizer of natural factors of an ergodic group extension of a rotation determine all factors
• Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics
• Almost Full Entropy Subshifts Uncorrelated to the Möbius Function
• Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
• Automatic sequences are orthogonal to aperiodic multiplicative functions

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