Arguments of zeros of highly log concave polynomials

David Handelman

For a real polynomial $p={\sum }_{i=0}^n{c}_i{x}^i$ with no negative coefficients and $n\ge 6$, let $\beta (p)={\inf }_{i=1}^{n-1}{c}_i^2/c_{i+1}{c}_{i-1}$ (so $\beta (p)\ge 1$ entails that $p$…