A Class of Littlewood Polynomials that are Not Lα-Flat

Uniform distribution theory Pub Date : 2020-06-01 DOI:10.2478/udt-2020-0003

E. Abdalaoui, M. Nadkarni

引用次数: 2

Abstract

Abstract We exhibit a class of Littlewood polynomials that are not Lα-flat for any α ≥ 0. Indeed, it is shown that the sequence of Littlewood polynomials is not Lα-flat, α ≥ 0, when the frequency of −1 is not in the interval ] 14 {1 \over 4} , 34 {3 \over 4} [ We further obtain a generalization of Jensen-Jensen-Hoholdt’s result by establishing that the sequence of Littlewood polynomials is not Lα-flat for any α> 2 if the frequency of −1 is not 12 {1 \over 2} . Finally, we prove that the sequence of palindromic Littlewood polynomials with even degrees are not Lα-flat for any α ≥ 0, and we provide a lemma on the existence of c-flat polynomials.

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一类非l α-平坦的Littlewood多项式

摘要我们证明了一类对于任意α≥0都不是l α-平坦的Littlewood多项式。事实上，证明了当- 1的频率不在14{1 \ / 4}，34{3 \ / 4}区间内时，Littlewood多项式的序列不是l α-平坦的，α≥0。我们进一步推广了Jensen-Jensen-Hoholdt的结果，即当- 1的频率不在12{1 \ / 2}时，对于任何α> 2, Littlewood多项式的序列都不是l α-平坦的。最后，我们证明了偶数次的回文Littlewood多项式序列对于任意α≥0都不是l α-平坦的，并给出了c-平坦多项式存在的一个引理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Uniform distribution theory

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