The eventual vanishing criterion for Hessian-nilpotent formal power series
Let P(z)∈C[[z]]P(z)\in {\mathbb C}[[z]]P(z)∈C[[z]] satisfy o(P(z))≥2o(P(z))\geq 2o(P(z))≥2, and write HesP(z)\operatorname{Hes}P(z)HesP(z) for its Hessian matrix. The series P(z)P(z)P(z) is Hessian nilpotent when…