E. H. el Abdalaoui

OpenAI partially disproves Littlewood's 1961 $L^\alpha$-flat theorem

We present a counterexample, produced by OpenAI, to Littlewood's 1961 theorem on $L^\alpha$-flat polynomials. The theorem asserts that no $L^\alpha$-flat polynomials exist within the class of trigonometric polynomials of the form$$\sum_{m=1}^{n} a_m \cos(m\theta+\alpha_m), \qquad n \in \mathbb{N}^*,$$satisfying$$k\, n^...