Some Results on the Vanishing Conjecture of Differential Operators with Constant Coefficients

Abstract

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 [Zh3] by the third named author. We also give two examples to show that the generalizations of both the vanishing conjecture and the Duistermaat-van der Kallen theorem [DK] to Laurent formal power series do not hold in general.

Minor improvements. Latex 21 pages

References in corpus (2)

• A Vanishing Conjecture on Differential Operators with Constant Coefficients
• Two Results on Homogeneous Hessian Nilpotent Polynomials

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• A case of the generalized vanishing conjecture