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.References
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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
- 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 - © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 79 (2010), 365-381
- MSC (2000): Primary 30F99; Secondary 05E35, 30C30, 58C15
- DOI: https://doi.org/10.1090/S0025-5718-09-02265-0
- MathSciNet review: 2552231