A Class of Littlewood Polynomials that are Not L α -Flat-Reference-Cited by-同舟云学术

A Class of Littlewood Polynomials that are Not L α -Flat

Published:2020-06-01 Issue:1 Volume:15 Page:51-74
ISSN:2309-5377
Container-title:Uniform distribution theory
language:en
Short-container-title:

Author:

Abdalaoui El Houcein El¹,Nadkarni Mahendra²

Affiliation:

1. Department of Mathematics , Normandy University of Rouen , LMRS UMR 6085 CNRS , France

2. Department of Mathematics , University of Mumbai , India

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/udt-2020-0003

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