Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

0-1 sequences of the Thue-Morse type and Sarnak’s conjecture
HTML articles powered by AMS MathViewer

by El Houcein El Abdalaoui, Stanisław Kasjan and Mariusz Lemańczyk PDF
Proc. Amer. Math. Soc. 144 (2016), 161-176 Request permission

Abstract:

We prove that the images via $z\mapsto z^m$ of the continuous part of the spectral measures of the dynamical systems generated by the 0-1 sequences of the Thue-Morse type are pairwise mutually singular for different odd numbers $m\in \mathbb {N}$. Sarnak’s conjecture on orthogonality with the Möbius function is proved to hold for such dynamical systems. A step toward the proof of this result is the observation that in the class of uniquely ergodic models of a fixed coalescent automorphism, the conjecture is stable under continuous extensions. In particular, Sarnak’s conjecture holds for all dynamical systems given by regular Toeplitz sequences. A non-regular Toeplitz sequence which is not orthogonal to the Möbius function is constructed.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 37B05, 47A40
  • Retrieve articles in all journals with MSC (2010): 37B05, 47A40
Additional Information
  • El Houcein El Abdalaoui
  • Affiliation: Laboratoire de Mathématiques Raphaël Salem, Normandie Université, Université de Rouen, CNRS, Avenue de l’Université, 76801 Saint Étienne du Rouvray, France
  • Email: elhoucein.elabdalaoui@univ-rouen.fr
  • Stanisław Kasjan
  • Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, 12/18 Chopin Street, 87-100 Toruń, Poland
  • MR Author ID: 333741
  • Email: skasjan@mat.umk.pl
  • Mariusz Lemańczyk
  • Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, 12/18 Chopin Street, 87-100 Toruń, Poland
  • MR Author ID: 112360
  • Email: mlem@mat.umk.pl
  • Received by editor(s): September 5, 2014
  • Received by editor(s) in revised form: November 25, 2014
  • Published electronically: June 23, 2015
  • Additional Notes: The third author’s research was supported by Narodowe Centrum Nauki grant DEC-2011/03/B/ST1/00407.
  • Communicated by: Nimish Shah
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 161-176
  • MSC (2010): Primary 37B05; Secondary 47A40
  • DOI: https://doi.org/10.1090/proc/12683
  • MathSciNet review: 3415586