Approche galoisienne de la transcendance diff\'erentielle

Abstract

In this survey we present the parameterized Galois theory of difference equations, as introduced by Hardouin-Singer. The purpose of this theory is to give a systematic approach to differential transcendence, also called hypertranscendence. As an example of the applications, we explain the Galoisian proof of H\"older's theorem on the differential transcendence of the Gamma function.