29 citations · 58 across the 9 of their papers we have counts for
10 papers
A note on Sarnak processes
Mariusz Lemańczyk, Michal D. Lemańczyk, Thierry de La Rue
Basic properties of stationary processes called Sarnak processes are studied. As an application, a combinatorial reformulation of Sarnak's conjecture on M{ö}bius orthogonality is p…
On the local Fourier uniformity problem for small sets
Adam Kanigowski, Mariusz Lemańczyk, Florian Karl Richter +1
We consider vanishing properties of exponential sums of the Liouville function of the form $$ \lim_{H\to\infty}\limsup_{X\to\infty}\frac{1}{\log X}\sum_{m\leq X}\frac{1}{m}\sup…
Furstenberg systems of pretentious and MRT multiplicative functions
Nikos Frantzikinakis, Mariusz Lemańczyk, Thierry de la Rue
We prove structural results for measure preserving systems, called Furstenberg systems, naturally associated with bounded multiplicative functions. We show that for all pretentious…
Dynamics of -free systems generated by Behrend sets. I
Stanisław Kasjan, Mariusz Lemańczyk, Sebastian Zuniga Alterman
We study the complexity of -free subshifts which are proximal and of zero entropy. Such subshifts are generated by Behrend sets. The complexity is shown to achieve any…
On arithmetic functions orthogonal to deterministic sequences
Adam Kanigowski, Joanna Kulaga-Przymus, Mariusz Lemańczyk +1
We prove Veech's conjecture on the equivalence of Sarnak's conjecture on Möbius orthogonality with a Kolmogorov type property of Furstenberg systems of the M\''obius function. This…
A generalization of Kátai's orthogonality criterion with applications
V. Bergelson, J. Kułaga-Przymus, M. Lemańczyk +1
We study properties of arithmetic sets coming from multiplicative number theory and obtain applications in the theory of uniform distribution and ergodic theory. Our main theorem i…
Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics
Vitaly Bergelson, Joanna Kułaga-Przymus, Mariusz Lemańczyk +1
A set is called rational if it is well-approximable by finite unions of arithmetic progressions. Examples of rational sets include many classical sets of numb…
On one-parameter Koopman groups
A. F. M. ter Elst, M. Lemanczyk
We characterize Koopman one-parameter -groups in the class of all unitary one-parameter -groups on as those that preserve and for which the infinit…
The Moebius function and continuous extensions of rotations
Joanna Kułaga-Przymus, Mariusz Lemańczyk
Let be of class for some and let . We show that for a generic , the extension $T_{c,f}\colon \mat…
Rigidity and Non-recurrence along Sequences
V. Bergelson, A. del Junco, M. Lemańczyk +1
Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do n…