13 citations · 23 across the 19 of their papers we have counts for
20 papers
A generalization of Littlewood's flat theorem,
el Houcein el Abdalaoui
We establish a generalization of Littlewood's criterion on -flatness by proving that there is no -flat polynomials, , within the class of analytic polynomials on the…
On -flatness of Erdős-Littlewood's polynomials
el Houcein el Abdalaoui
It is shown that Erdös--Littlewood's polynomials are not -flat when is an even integer (and hence for any ). This provides a partial solution to an old problem…
Möbius random law and infinite rank-one maps
e. H. el Abdalaoui, Cesar E. Silva
We prove that Sarnak's conjecture holds for any infinite measure symbolic rank-one map. We further extended Bourgain-Sarnak's result, which says that the Möbius function is a good…
A disproof of polynomials Rudin conjecture,
el Houcein el Abdalaoui
It is shown that the -norms polynomials Rudin conjecture fails. Our counterexample is inspired by Bourgain's work on NLS. Precisely, his study of the Strichartz's inequality o…
Van der Corput inequality for real line and Wiener-Wintner theorem for amenable groups
el Houcein el Abdalaoui
We extend the classical van der Corput inequality to the real line. As a consequence, we obtain a simple proof of the Wiener-Wintner theorem for the -action which asser…
On the symmetric version of Seaki Theorem and flat densities
el Houcein el Abdalaoui
It is shown that for any there exists a symmetric probability measure on the torus such that the Hausdorff dimension of the support of is and i…