June, 2020

51-74

El Houcein El Abdalaoui and Mahendra Nadkarni

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 ]14, 34[ 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 12. 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.

Abdalaoui, E.H.E. & Nadkarni, M. (2020). A Class of Littlewood Polynomials that are Not Lα-Flat. Uniform distribution theory, 15(1), 51-74. https://doi.org/10.2478/udt-2020-0003