Abstract
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 ] 1 4 {1 \over 4} , 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 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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