Zobrazeno 1 - 10
of 174
pro vyhledávání: '"Lemańczyk, Mariusz"'
We solve Boshernitzan's problem of characterization (in terms of so called Furstenberg systems) of bounded sequences that are orthogonal to all uniquely ergodic systems. Some variations of Boshernitzan's problem involving characteristic classes are c
Externí odkaz:
http://arxiv.org/abs/2404.07907
Basic properties of stationary processes called Sarnak processes are studied. As an application, a combinatorial reformulation of Sarnak's conjecture on M{\"o}bius orthogonality is provided.
Externí odkaz:
http://arxiv.org/abs/2403.20054
Publikováno v:
Int. Math. Res. Not. IMRN (2), 11488-11512, 2024
We consider vanishing properties of exponential sums of the Liouville function $\lambda$ of the form $$ \lim_{H\to\infty}\limsup_{X\to\infty}\frac{1}{\log X}\sum_{m\leq X}\frac{1}{m}\sup_{\alpha\in C}\bigg|\frac{1}{H}\sum_{h\leq H}\lambda(m+h)e^{2\pi
Externí odkaz:
http://arxiv.org/abs/2310.05528
We prove structural results for measure preserving systems, called Furstenberg systems, naturally associated with bounded multiplicative functions. We show that for all pretentious multiplicative functions these systems always have rational discrete
Externí odkaz:
http://arxiv.org/abs/2304.03121
Publikováno v:
Acta Arithmetica 209 (2023), 135-171
We study the complexity of $\mathscr{B}$-free subshifts which are proximal and of zero entropy. Such subshifts are generated by Behrend sets. The complexity is shown to achieve any subexponential growth and is estimated for some classical subshifts (
Externí odkaz:
http://arxiv.org/abs/2205.08273
We prove that on B-free subshifts, with B satisfying the Erd\"os condition, all cellular automata are determined by monotone sliding block codes. In particular, this implies the validity of the Garden of Eden theorem for such systems.
Comment: 2
Comment: 2
Externí odkaz:
http://arxiv.org/abs/2106.14673
We prove Veech's conjecture on the equivalence of Sarnak's conjecture on M\"obius orthogonality with a Kolmogorov type property of Furstenberg systems of the M\''obius function. This yields a combinatorial condition on the M\"obius function itself wh
Externí odkaz:
http://arxiv.org/abs/2105.11737
Autor:
Kanigowski, Adam, Lemańczyk, Mariusz
This is a survey on spectral theory of dynamical systems.
Externí odkaz:
http://arxiv.org/abs/2006.11616
It is shown that in a class of counterexamples to Elliott's conjecture by Matomaki, Radziwill and Tao, the Chowla conjecture holds along a subsequence.
Externí odkaz:
http://arxiv.org/abs/2006.09958