On the van der Corput's $k$-th derivative test for exponential sums

Olivier Robert 1
1 CTN - Combinatoire, théorie des nombres
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We give an overview of van der Corput's method for exponential sums, with a particular interest for the simplest estimates with the $k$-thderivative test. We study the optimality of the results and we present recent improvements.
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Olivier Robert. On the van der Corput's $k$-th derivative test for exponential sums. Indagationes Mathematicae, Elsevier, 2015, pp.559-589. ⟨www.elsevier.com/locate/indag⟩. ⟨10.1016/j.indag.2015.11.009⟩. ⟨hal-01464831⟩

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