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

Olivier Robert (1, 2)

1 ICJ - Institut Camille Jordan
2 CTN - Combinatoire, théorie des nombres

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.

Mots clés: Exponential sums; Van der Corput's method; Diophantine systems

Domaines: Théorie des nombres [math.NT]

Olivier Robert. On the van der Corput's $k$-th derivative test for exponential sums. Indagationes Mathematicae, 2015, 27, pp.559-589. ⟨10.1016/j.indag.2015.11.009⟩. ⟨hal-01464831⟩