A fourth derivative test for exponential sums

O Robert; P Sargos

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arXiv · 2307.03562

A fourth derivative test for exponential sums

O Robert·P Sargos

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Abstract

We give an upper bound for the exponential $\sum_{m=1}^M \exp( 2i\pi f (m))$ in terms of $M$ and $\lambda$, where $\lambda$ is a small positive number which denotes the size of the fourth derivative of the real valued function $f$. The classical van der Corput's exponent 1/14 is improved into 1/13 by reducing the problem to a mean square value theorem for triple exponential sums.

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O Robert, P Sargos. 2023-07-07. A fourth derivative test for exponential sums. https://arxiv.org/abs/2307.03562

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