60 citations · 97 across the 30 of their papers we have counts for
5 papers · 1 filter
A dynamical point of view on the set of B-free integers
El Houcein El Abdalaoui, Mariusz Lemanczyk, Thierry De La Rue
We extend the study of the square-free flow, recently introduced by Sarnak, to the more general context of B-free integers, that is to say integers with no factor in a given family…
Calculus of Generalized Riesz Products
e. H. el Abdalaoui, M. G. Nadkarni
In this paper we discuss generalized Riesz products bringing into consideration theory, the notion of Mahler measure, and the zeros of polynomials appearing in the generalize…
Spectral properties of the Möbius function and a random Möbius model
E. H. el Abdalaoui, M. Disertori
Assuming Sarnak conjecture is true for any singular dynamical process, we prove that the spectral measure of the Möbius function is equivalent to Lebesgue measure. Conversely, unde…
0-1 sequences of the Thue-Morse type and Sarnak's conjecture
El Houcein El Abdalaoui, Stanisław Kasjan, Mariusz Lemańczyk
We show that the images via of the continuous part of the spectral measures of the dynamical systems generated by the 0-1 sequences of the Thue-Morse type are pairwi…
On spectral disjointness of powers for rank-one transformations and Möbius orthogonality
El Houcein El Abdalaoui, Mariusz Lemanczyk, Thierry De La Rue
We study the spectral disjointness of the powers of a rank-one transformation. For a large class of rank-one constructions, including those for which the cutting and stacking param…