Barry Simon Fine Structure of the Zeros of Orthogonal Polynomials, II. OPUC With Competing Exponential Decay (276K, pdf) ABSTRACT. We present a complete theory of the asymptotics of the zeros of OPUC with Verblunsky coefficients $\alpha_n = \sum_{\ell=1}^L C_\ell b_\ell^n + O((b\Delta)^n)$ where $\Delta <1$ and $|b_\ell| = b<1$.