log-concavity

Let $p(x_1,…,x_m) = \sum_{r_1 + \cdots + r_m = n} a_{r_1,…,r_m} \prod_{1 \leq i \leq m } x_i^{r_{i}}$ be a homogeneous polynomial of degree $n$ in $m$ variables. We call such polynomial {\bf H-Stable} if $p(z_1,…,z_m) \neq 0$ provided that the real parts $Re(z_i) > 0: 1 \leq i \leq m$. It can be assumed … Read more