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Computation of conformal representations of compact Riemann surfaces
Author(s):
Guillermo
López
Lagomasino;
Domingo
Pestana;
José
M.
Rodríguez;
Dmitry
Yakubovich.
Journal:
Math. Comp.
79
(2010),
365-381.
MSC (2000):
Primary 30F99;
Secondary 05E35, 30C30, 58C15
Posted:
June 4, 2009
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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.
References:
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- A.I. Aptekarev, G. López Lagomasino, and I.A. Rocha, Asymptotic behavier of the ratio of Hermite-Padé polynomials for Nikishin systems, Mat. Sb. 196 (2005), 1089-1107. MR 2188362 (2006h:41040)
- 2.
- A.I. Aptekarev, V. Kalyagin, G. López Lagomasino, and I.A. Rocha, On the limit behavior of recurrence coefficients for multiple orthogonal polynomials, J. of Approx. Theory 139 (2006), 346-370. MR 2220045 (2007a:42048)
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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:
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
Posted:
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
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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