3 papers
math.DS2024
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…
math.DS2023
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…
math.DS2021
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…