Some Results on the Vanishing Conjecture of Differential Operators with Constant Coefficients
Commutative Algebra
2022-08-12 v2 Complex Variables
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.
Keywords
Cite
@article{arxiv.0903.1478,
title = {Some Results on the Vanishing Conjecture of Differential Operators with Constant Coefficients},
author = {Arno van den Essen and Roel Willems and Wenhua Zhao},
journal= {arXiv preprint arXiv:0903.1478},
year = {2022}
}
Comments
Minor improvements. Latex 21 pages