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Consider the product of complex linear monic polynomials times polynomials of degree less than $n$, that is $\big( (z-\lambda), p(z)\big)\mapsto (z-\lambda)p(z)$. If we represent a polynomial by its ...

Given two $n$-tuple vectors $\vec{\alpha}=(\alpha_1,\cdots,\alpha_n)$ and $\vec{h}=(h_1,\cdots,h_n)$, where $h_i\ge0$, $\sum_{i=1}^nh_i=1$, and $\alpha_i\in(0,1)$, we consider a random variable $S$ on ...