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

Arno van den Essen, Roel Willems and Wenhua Zhao
Arxiv ID: 0903.1478Last updated: 8/12/2022
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.

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