An application of van der Corput's inequality
type: Item
instance of: scholarly article
zbMATH Open document ID: 0998.11044
author: Kanthi Perera
publication date: 2001-05-13T00:00:00Z
full work available at URL: https://eudml.org/doc/122155
Mathematics Subject Classification ID: 11L07
zbMATH DE Number: 1589369
zbMATH Keywords: van der Corput's inequality
zbMATH Keywords: Hardy-Littlewood result
MaRDI profile type: Publication
title: An application of van der Corput's inequality
published in: JIPAM. Journal of Inequalities in Pure \& Applied Mathematics
review text: The author gives a short and elegant proof of the following result: Let \(\beta\) be a nonnegative real number. Then NEWLINE\[NEWLINE \sum_{k=1}^n k^{\beta} \exp ( i( \omega k + \alpha k^2))= o(n^{\beta +1}), NEWLINE\]NEWLINE uniformly in \(\omega\), when \(\alpha\) is not a rational multiple of \(\pi\). The main tool of the proof is an inequality, due to van der Corput.
reviewed by: Jürgen Hinz
description: scientific article