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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computation of conformal representations of compact Riemann surfaces


Authors: Guillermo López Lagomasino, Domingo Pestana, José M. Rodríguez and Dmitry Yakubovich
Journal: Math. Comp. 79 (2010), 365-381
MSC (2000): Primary 30F99; Secondary 05E35, 30C30, 58C15
Published electronically: June 4, 2009
MathSciNet review: 2552231
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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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Additional Information

Guillermo López Lagomasino
Affiliation: Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganes, Spain
Email: lago@math.uc3m.es

Domingo Pestana
Affiliation: Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganes, Spain
Email: dompes@math.uc3m.es

José M. Rodríguez
Affiliation: Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganes, Spain
Email: jomaro@math.uc3m.es

Dmitry Yakubovich
Affiliation: Department of Mathematics, Universidad, Autónoma de Madrid and Instituto de Ciencias, Mathemáticas (CSIC-UAM-UC3M-UCM), Madrid, Spain
Email: dmitry.yakubovich@uam.es

DOI: http://dx.doi.org/10.1090/S0025-5718-09-02265-0
PII: S 0025-5718(09)02265-0
Keywords: Orthogonal polynomials, compact Riemann surfaces, branched covering, nonlinear equations, Newtonian continuation method.
Received by editor(s): October 21, 2008
Received by editor(s) in revised form: February 13, 2009
Published electronically: June 4, 2009
Additional Notes: The first, second, and third authors’ research was partially supported by a grant from M.E.C. (MTM 2006-13000-C03-02) and a grant from U.C.III M./C.A.M. (CCG07-UC3M/ESP-3339), Spain
The second and third authors’ research was partially supported by two grants from M.E.C. (MTM 2006-11976 and MTM 2007-30904-E), Spain
The fourth author’s research was partially supported by the Grant MTM2008-06621-C02-01, DGI-FEDER, of the Ministry of Science and Innovation, Spain
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.