Computation of conformal representations of compact Riemann surfaces

Details Computation of conformal representations of compact Riemann surfaces Computation of conformal representations of compact Riemann surfaces

2009-03-03

arxiv.org/abs/0903.0508v1

Math. Comp. 79 (2010), no. 269, 365-381

Mathematics

Complex Variables

To appear in Mathematics of Computation

Scientific paper

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.

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