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math.NT2026
OpenAI partially disproves Littlewood's 1961 -flat theorem
el Houcein el Abdalaoui
We present a counterexample, produced by OpenAI, to Littlewood's 1961 theorem on -flat polynomials. The theorem asserts that no -flat polynomials exist within the class o…
math.DS2026
On the spectral analysis of dynamical Möbius-Sarnak process and topological entropy of Möbius fonction
el Houcein el Abdalaoui
By extending the Rokhlin-Sinai machinery relating to the entropy and countable Lebesgue component in the spectrum, we establish that the dynamical Möbius-Sarnak process has a count…
math.DS2026
Operator ergodic theorems with Möbius "weights"
El Houcein El Abdalaoui, Michael Lin
Motivated by Sarnak's conjecture in topological dynamics for the Möbius function , we study, for a power-bounded on a Banach space , the weak convergence $$ (*) \qquad \q…