Computation of conformal representations of compact Riemann surfaces

Lagomasino, Guillermo; Pestana, Domingo; Rodríguez, José; Yakubovich, Dmitry

doi:10.1090/S0025-5718-09-02265-0

Computation of conformal representations of compact Riemann surfaces
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by Guillermo López Lagomasino, Domingo Pestana, José M. Rodríguez and Dmitry Yakubovich PDF

Math. Comp. 79 (2010), 365-381 Request permission

Abstract:

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.

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