Abstract
In this paper, we study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms have the same nth root behavior as the weighted norms for certain extremal polynomials. Our results include as special cases several of the previous results of Erdős, Freud, Jentzsch, Szegő and Blatt, Saff, and Simkani. Applications are given concerning the zeros of orthogonal polynomials over a smooth Jordan curve (in particular, on the unit circle) and the zeros of polynomials of best approximation on R to nonentire functions.
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