Computation of conformal representations of compact Riemann surfaces

Abstract

We find a system of two polynomial equations in two unknowns, whose solution allows 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.

To appear in Mathematics of Computation

Cited by in corpus (3)

• Riemann-Hilbert analysis for a Nikishin system
• Hyperelliptic uniformization of algebraic curves of the third order
• Asymptotics of multiple orthogonal polynomials for a system of two measures supported on a starlike set