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

@article{citeulike:4161878, abstract = {In this paper we prove four cases for 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 author. We will also give two counter-examples to show that both the vanishing conjecture and Duistermaat and van der Kallen's theorem [DK] fail in the setting of (Laurent) formal power series.}, archivePrefix = {arXiv}, author = {van den Essen, Arno and Willems, Roel and Zhao, Wenhua}, citeulike-article-id = {4161878}, citeulike-linkout-0 = {http://arxiv.org/abs/0903.1478}, citeulike-linkout-1 = {http://arxiv.org/pdf/0903.1478}, eprint = {0903.1478}, keywords = {commutative\_algebra, complex\_analysis, linear\_systems, univariate\_functions}, month = {Mar}, posted-at = {2009-03-10 17:20:32}, priority = {4}, title = {Some Results on the Vanishing Conjecture of Differential Operators with Constant Coefficients}, url = {http://arxiv.org/abs/0903.1478}, year = {2009} }

TY - JOUR ID - citeulike:4161878 L3 - citeulike-article-id:4161878 N2 - In this paper we prove four cases for 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 author. We will also give two counter-examples to show that both the vanishing conjecture and Duistermaat and van der Kallen's theorem [DK] fail in the setting of (Laurent) formal power series. TI - Some Results on the Vanishing Conjecture of Differential Operators with Constant Coefficients KW - commutative_algebra KW - complex_analysis KW - linear_systems KW - univariate_functions AU - van den Essen, Arno AU - Willems, Roel AU - Zhao, Wenhua PY - 2009/Mar/09/ UR - http://arxiv.org/abs/0903.1478 ER -