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el Houcein el Abdalaoui, On L^alpha-flatness of Erdős-Littlewood's polynomials. arXiv preprint (2025). arXiv:2504.21499, doi:10.48550/arXiv.2504.21499.
Read from the arXiv abstract page only; no PDF was consulted. The preprint asserts that Erdos-Littlewood polynomials, those with plus-or-minus-one coefficients, fail to be L^alpha-flat whenever alpha > 2 is an even integer, and therefore for all alpha at least 4, which the author presents as a partial answer to an old problem of Littlewood and as a positive answer to the Erdos-Newman conjecture that no ultraflat sequence of such polynomials exists. The stated method is short: the classical bound for L^p norms of the Dirichlet kernel, the Marcinkiewicz-Zygmund interpolation inequalities, and the p-concentration theorem of Bonami and Revesz. For problem 1150 this would settle the associated prize conjecture, but Thomas Bloom and Terence Tao reportedly found serious flaws, specifically that the argument on page 9 does not in fact contradict the paper's own Lemma 5, so the claim is treated as unconfirmed and probably unfixable. No verified theorem statements were obtained.
Source: https://arxiv.org/abs/2504.21499.