A Class of Littlewood Polynomials that are Not Lα-Flat

El Houcein El Abdalaoui; Mahendra Nadkarni

doi:10.2478/udt-2020-0003

Abstract

We exhibit a class of Littlewood polynomials that are not L^α-flat for any α ≥ 0. Indeed, it is shown that the sequence of Littlewood polynomials is not L^α-flat, α ≥ 0, when the frequency of −1 is not in the interval ] $\frac{1}{4}$ {1 \over 4}, $\frac{3}{4}$ {3 \over 4}[ We further obtain a generalization of Jensen-Jensen-Hoholdt’s result by establishing that the sequence of Littlewood polynomials is not L^α-flat for any α> 2 if the frequency of −1 is not $\frac{1}{2}$ {1 \over 2}. Finally, we prove that the sequence of palindromic Littlewood polynomials with even degrees are not L^α-flat for any α ≥ 0, and we provide a lemma on the existence of c-flat polynomials.

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A Class of Littlewood Polynomials that are Not Lα-Flat

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