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

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

2009-03-09

arxiv.org/abs/0903.1478v2

Mathematics

Commutative Algebra

Minor improvements. Latex 21 pages

Scientific paper

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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