ON ROOTS OF RANDOM POLYNOMIALS

We study the distribution of the complex roots of random polynomials o f degree n with i.i.d. coefficients. Using techniques related to Rice' s treatment of the real roots question, we derive, under appropriate m oment and regularity conditions, an exact formula for the average dens ity of this distribution, which yields appropriate limit average densi ties. Further, using a different technique, we prove limit distributio n results for coefficients in the domain of attraction of the stable l aw.