Discrepancy of Signed Measures and Polynomial Approximation

Jentzsch [91] showed that every point of the circle of convergence of apower series is a limit point of zeros of its partial sums. if almost all zeros of the polynomials of best 2 approximation to f (in a weighted L -norm) are outside of an open ellipse c with foci at -1 and 1, then f has a continuous extension that is analytic in c.