COMPLEX ROOTS OF A RANDOM ALGEBRAIC POLYNOMIAL

This pager, for any constant K, provides an exact formula for the aver age density of the distribution of the complex roots of equation eta(0 ) + eta(1)z + eta(2)z(2) + ... + eta(n-1)Z(n-1) = K where eta(j) = a(j ) + ib(j) and {a(j)}(j=0)(n-1) and {b(j)}(j=0)(n-1) are sequences of i ndependent identically and normally distributed random variables and K is a complex number with K as its real and imaginary parts. The case of real roots of the above equation with real coefficients and K, z is an element of R is well known. Further we obtain the limiting behavio ur of this distribution function as n tends to infinity. (C) 1997 Acad emic Press.