ON THE ZEROS OF SEQUENCES OF POLYNOMIALS

In this paper we generalize a result of Blatt, Saff, and Simkani on the limit distribution of zeros of sequences of polynomials. In a typical application these polynomials converge on a compact subset E of the complex plane. The highest coefficient of the polynomials plays an important role in the theorem of Blatt, Saff, and Simkani. In this paper we replace the behavior of the highest coefficient by the behavior of the sequence on some compact set in C\E. Furthermore we show how this generalization can be applied to sequences of maximally convergent polynomials. © 1990.