Szegő polynomials: a view from the Riemann-Hilbert window Martínez-Finkelshtein, A. Zeros Asymptotics Riemann-Hilbert problem Szegő polynomials Verblunsky coefficients This is an expanded version of the talk given at the conference “Constructive Functions Tech-04”. We survey some recent results on canonical representation and asymptotic behavior of polynomials orthogonal on the unit circle with respect to an analytic weight. These results are obtained using the steepest descent method based on the Riemann-Hilbert characterization of these polynomials. 2014-07-16T09:55:39Z 2014-07-16T09:55:39Z 2006 info:eu-repo/semantics/article Martínez-Finkelshtein, A. Szegő polynomials: a view from the Riemann-Hilbert window. Electronic Transactions on Numerical Analysis, 256: 369-392 (2006). [http://hdl.handle.net/10481/32691] 1068-9613 http://hdl.handle.net/10481/32691 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ info:eu-repo/semantics/openAccess Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Kent State University. Institute of Computational Mathematics