Correlations between real and complex zeros of a random polynomial

Consider a random polynomial $G(z):=ξ_0+ξ_1z+\dots+ξ_nz^n,\quad z\in\mathbb{C},$ where $ξ_0,ξ_1,\dots,ξ_{n}$ are independent real-valued random variables with probability density functions $f_0,\dots,f_n$. We give an explicit formula for the mixed $(k,l)$-correlation function $ρ_{k,l}:\mathbb{R}^k\times\mathbb{C}_+^l \to\mathbb{R}_+$ between $k$ real and $l$ complex zeros of $G_n$.

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