Computation of conformal representations of compact Riemann surfaces

We find a system of two polynomial equations in two unknowns, whose solution allows us to give an explicit expression of the conformal representation of a simply connected three-sheeted compact Riemann surface onto the extended complex plane. This function appears in the description of the ratio asymptotic of multiple orthogonal polynomials with respect to so-called Nikishin systems of two measures.

• Type: Journal
• Year: 2010
• Where: MOC
• Authors: Guillermo López Lagomasino, Domingo Pestana, José M. Rodríguez, Dmitry Yakubovich
• Keywords: Compact Riemann Surface, Extended Complex Plane, MOC 2010, Multiple Orthogonal Polynomials, Security Privacy