Some Notes on Flat Polynomials

E. H. El Abdalaoui; M. G. Nadkarni

Some Notes on Flat Polynomials

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arxiv 1402.5457 v1 pith:SSHO3GAS submitted 2014-02-22 math.CV math.DSmath.SP

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

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keywords polynomialsflatconditionnecessarysequencesomealmostconnection

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abstract

Connection of flat polynomials with some spectral questions in ergodic theory is discussed. A necessary condition for a sequence of polynomials of the type $\frac{1}{\sqrt{N}} \big(1 +\sum_{j=1}^{N-1} z^{n_j}\big)$ to be flat in almost everywhere sense is given, which contrasts with a similar necessary condition for a sequence of polynomials to be ultraflat.

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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.

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