Some results on the vanishing conjecture of differential operators with constant coefficients

• Arno van den Essen ^[2] ; Roel Willems ^[2] ; Wenhua Zhao ^[1]
  1. [1] Illinois State University

     Illinois State University

     Township of Normal, Estados Unidos

     
  2. [2] Radboud University Nijmegen, The Netherlands
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 9 (September 2015), 2015, págs. 3847-3861
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.12.024
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• Resumen

  • 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 [15] by the third named author. We also give two examples to show that both the Vanishing Conjecture and the Duistermaat–van der Kallen Theorem [6] cannot be generalized to the setting of (Laurent) formal power series in general.