An application of van der Corput's inequality (Q2710143)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: An application of van der Corput's inequality |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An application of van der Corput's inequality |
scientific article |
Statements
13 May 2001
0 references
van der Corput's inequality
0 references
Hardy-Littlewood result
0 references
An application of van der Corput's inequality (English)
0 references
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.
0 references
