Computation of Conformal Representations of Compact Riemann Surfaces Articles uri icon

publication date

  • January 2010

start page

  • 365

end page

  • 381

issue

  • 269

volume

  • 79

international standard serial number (ISSN)

  • 0025-5718

electronic international standard serial number (EISSN)

  • 1088-6842

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.