3 papers
math.NT2024
Furstenberg systems of pretentious and MRT multiplicative functions
Nikos Frantzikinakis, Mariusz LemaÅczyk, 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…
math.DS2024
On the local Fourier uniformity problem for small sets
Adam Kanigowski, Mariusz LemaÅczyk, 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}\su…
math.DS2024
A note on Sarnak processes
Mariusz LemaÅczyk, Michal D. LemaÅczyk, 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…