Joint work with Friedrich G\"otze, Ildar Ibragimov, and Alexander Nazarov.
Let $\xi_0,\xi_1,\dots,\xi_n,\dots$ be a sequence of random variables.
We assume that these variables are independent, identically
distributed, and
nondegenerate.
Consider a random polynomial of one variable
\[
G_n(t)=\xi_0+\xi_1t+\dots+\xi_{n-1} t^{n-1} +\xi_n t^n.
\]
We consider two natural questions: how many roots of $G_n$ are real in
average and what is the asymptotical distribution of complex roots of
$G_n$?
