Determining the first radii of meromorphy via orthogonal polynomials on the unit circle

Applying a result concerning a convergence of modified orthogonal Padé approximants constructed from orthogonal polynomials on the unit circle, we prove an analogue of Hadamard’s theorem for determining the radius of 1-meromorphy of a function holomorphic on the closed unit disk. Furthermore, we apply our result to study analytic properties of the reciprocal of Szego ̋ functions when their corresponding sequence of Verblunsky coefficients has exponential decay.