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.

Computation of Conformal Representations of Compact Riemann Surfaces Articles