Two Results on Homogeneous Hessian Nilpotent Polynomials

Arno van den Essen, Wenhua Zhao

Let $z=(z_1,...,z_n)$ and $\Delta ={\sum }_{i=1}^n\frac{{\partial }^2}{\partial z_i^2}$ the Laplace operator. A formal power series $P(z)$ is said to be {\it Hessian Nilpotent}(HN) if its…