Abstract :

Van der Corput lemma is an interesting tool to analyse in a quick and simple manner the rough behaviour of oscillatory integrals. However, its original statement fails to work in the picture of several variables, forcing us to use stationary phase approximation. In this talk, we present both methods through the study of a particularly interesting exemple in two variables. In this exemple stationary phase methods fail to achieve the correct asymptotics, but Van der Corput lemma can be adapted to capture the correct result.