domain of attraction of normal law and zeros of random polynomials

let$ p_{n}(x)= sum_{i=0}^{n} a_{i}x^{i}$ be a random algebraicpolynomial, where $a_{0},a_{1}, cdots $ is a sequence of independent random variables belong to the domain of attraction of the normal law. thus $a_j$'s for $j=0,1cdots $ possesses the characteristic functions $exp {-frac{1}{2}t^{2}h_{j}(t)}$, where $h_j(t)$'s are complex slowlyvarying functions.under the assumption that there exist a real positive slowly varyingfunction $h(cdot)$ and positive constants $t_{0}$, $ c_{ast}$ and$c^{ast}$ that $c_{ast}h(t) leq mbox{re}[h_{j}(t)] leq c^{ast} h(t),;tleqt_{0},;j=1,cdots,n$, we find thatwhile the variance of coefficients are bounded, real zeros are concentrated around $pm 1$, and the expected number of realzeros of $p_n(x)$ round the origin at a distance $(log n)^(-s)$ of $pm 1$ are at most of order $oleft( (log n)^s log (log n)right)$.