E. H. el Abdalaoui

activity

20102026

most citedOn spectral disjointness of powers for rank-one transformations and Möbius orthogonality

60 citations · 97 across the 30 of their papers we have counts for

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math.NT2026

OpenAI partially disproves Littlewood's 1961 $L^{α}$ -flat theorem

el Houcein el Abdalaoui

We present a counterexample, produced by OpenAI, to Littlewood's 1961 theorem on $L^{α}$ -flat polynomials. The theorem asserts that no $L^{α}$ -flat polynomials exist within the class o…

math.NT2019

Exponential sums of the Möbius function and flat polynomials

el Houcein el Abdalaoui

We present an elementary problem on analytic polynomials with coefficients $\pm 1$ or in ${0, \pm 1}$ which implies Riemann hypothesis. It is turns out that this problem is a par…

math.NT2017

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 $x \mapsto (a x + b) / (c x + d)$ over a finite field of $…

math.NT2016

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

E. H. el Abdalaoui, M. G. Nadkarni

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, $α \geq 0$ …

OpenAI partially disproves Littlewood's 1961 Lα-flat theorem

Exponential sums of the Möbius function and flat polynomials

Disjointness of the Möbius Transformation and Möbius Function

A class of Littlewood polynomials that are not Lα-flat

OpenAI partially disproves Littlewood's 1961 $L^{α}$ -flat theorem

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