60 citations · 97 across the 30 of their papers we have counts for
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Disjointness of the Möbius Transformation and Möbius Function
El Houcein El Abdalaoui, Igor E. Shparlinski
We study the distribution of the sequence of elements of the discrete dynamical system generated by the Möbius transformation over a finite field of $…
On Veech's proof of Sarnak's theorem on the Möbius flow
el Houcein el Abdalaoui
We present Veech's proof of Sarnak's theorem on the Möbius flow which say that there is a unique admissible measure on the Möbius flow. As a consequence, we obtain that Sarnak's co…
On the homogeneous ergodic bilinear averages with Möbius and liouville weights
El Houcein El Abdalaoui
It is shown that the homogeneous ergodic bilinear averages with Möbius or Liouville weight converge almost surely to zero, that is, if is a map acting on a probability space $(…
Oscillating sequences, Gowers norms and Sarnak's conjecture
el Houcein el Abdalaoui
It is shown that there is an oscillating sequence of higher order which is not orthogonal to the class of dynamical flow with topological entropy zero. We further establish that an…
Möbius disjointness for models of an ergodic system and beyond
El Houcein El Abdalaoui, Joanna Kułaga-Przymus, Mariusz Lemańczyk +1
Given a topological dynamical system and an arithmetic function , we study the strong MOMO property (relatively to $\boldsymbol…