Resumen de Some results on the vanishing conjecture of differential operators with constant coefficients

A. van den Essen, Roel Willems, Wenhua Zhao

• In this paper we prove four cases of the Vanishing Conjecture of differential operators with constant coefficients and also a conjecture on the Laurent polynomials with no holomorphic parts, which were proposed in [15] by the third named author. We also give two examples to show that both the Vanishing Conjecture and the Duistermaat–van der Kallen Theorem [6] cannot be generalized to the setting of (Laurent) formal power series in general.