Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

EL Houcein El Abdalaoui  (e. H. e. A.)

Dear Cyber visitor,

Thanks you very much for visiting my homepage.

As a mathematecian, my research interest is Ergodic Theory and Dynamical Systems, Spectral Theory of Dynamical Systems, Julia sets and complex Analysis,Probability and Number Theory, and Harmonic Analysis and Fonctionnel Analysis. I also working on some class of PDE. 

In my recent work, I solved the The Banach Problem from the Scootich Book on finding a conservative dynamical system with simple Lebesgue spectrum, that is, there is a map T measure-preserving and acting on sigma-finite space and a square integerable function f such that the family {f o T^n}  is othronormal basis. I further establish that there exist a sequence of flat  polynomials with coefficients 0 and 1 ( a L^2-normalized sequence of polynomails is flat if it converge to the polynomial 1).

I recently also proved that if the L^p norm of the L^2-normalized polynomials with Liouville coefficients is bounded then Riemann hypothesis is true. Finaly, I just upload a paper on arxiv in which I prove that Chowla and Sarnak conjectures are equivalents (Chowla conjecture say that Liouville is normal and Sarnak that the Liouville  function is statistically orthogonal to any deterministic sequence.