arXiv subjects

E. H. el Abdalaoui

Publications and source records attributed to E. H. el Abdalaoui.

2 recordsLinked to original sources

arXiv2017

A class of Littlewood polynomials that are not $L^α$-flat

We exhibit a class of Littlewood polynomials that are not $L^α$-flat for any $α\geq 0$. Indeed, it is shown that the sequence of Littlewood polynomials is not $L^α$-flat, $α\geq 0$, when the frequency of $-1$ is not in the interval $]\frac14,\frac34[$. We further obtain a generalization of Jensen-Jensen-Hoholdt's result by establishing that the sequence of Littlewood polynomials is not $L^α$-flat for any $α> 2$ if the frequency of $-1$ is not $\frac12$. Finally, we prove that the sequence of palindromic Littlewood polynomials with even degrees are not $L^α$-flat for any $α\geq 0$.

math.NT↗

arXiv2013

Spectral properties of the Möbius function and a random Möbius model

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, under Elliott conjecture, we establish that the Möbius function is orthogonal to any uniquely ergodic dynamical system with singular spectrum. Furthermore, using Mirsky Theorem, we find a new simple proof of Cellarosi-Sinai Theorem on the orthogonality of the square of the Möbius function with respect to any weakly mixing dynamical system. Finally, we establish Sarnak conjecture for a particular random model.

math.DS↗