Tuen-Wai Ng, HKU, Hong Kong

Meromorphic solutions of higher order Briot-Bouquet differential equations

Abstract

In this talk, we shall prove the following result. Let y be a meromorphic function with at least one pole in the plane and y is neither elliptic nor degenerated elliptic. Then y and y^(k) are algebraically independent. This solves an old problem of Eremenko on higher order Briot−Bouquet differential equations. This is a joint work with A. Eremenko and L.W. Liao.