An application of van der Corput's inequality
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.
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