On flat polynomials with non-Negative coefficients

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e. H. el Abdalaoui , M. G. Nadkarni This is my paper · ORCID

classification math.DSmath.CVmath.NTmath.PRmath.SP

keywords coefficientsflatnon-negativepolynomialsanalyticconditionformulatenecessary

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We formulate and prove a necessary condition for a sequence of analytic trigonometric polynomials with real non-negative coefficients to be flat a.e.

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A generalization of Littlewood's $L^\alpha$ flat theorem, $\alpha>0$
math.NT 2025-09 reject novelty 7.0 of 10

Claims to confirm the L^α-Littlewood, L^1-Newman, and L^∞-Erdős conjectures via a short Clarkson-inequality argument, but the key norm-convergence step is unjustified.