Geodesic
Determination of the Polynomial Uniformizing a Given Compact Riemann Surface
Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 597-607.

Voir la notice de l'article provenant de la source Math-Net.Ru

An approximate method for finding the polynomial uniformizing a given Riemann surface is proposed. The method is based on joining this surface with another surface by a smooth curve in the space of branched coverings of the Riemann sphere for which the uniformizing polynomial is known. The critical points of the required polynomial are found by using the solutions of the Cauchy problem for the system of ordinary differential equations.
Keywords: Riemann surface, Riemann sphere, branched covering, uniformizing polynomial, Cauchy problem. 
@article{MZM_2012_91_4_a11,
     author = {S. R. Nasyrov},
     title = {Determination of the {Polynomial} {Uniformizing} a {Given} {Compact} {Riemann} {Surface}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {597--607},
     publisher = {mathdoc},
     volume = {91},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a11/}
}
TY  - JOUR
AU  - S. R. Nasyrov
TI  - Determination of the Polynomial Uniformizing a Given Compact Riemann Surface
JO  - Matematičeskie zametki
PY  - 2012
SP  - 597
EP  - 607
VL  - 91
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a11/
LA  - ru
ID  - MZM_2012_91_4_a11
ER  - 
%0 Journal Article
%A S. R. Nasyrov
%T Determination of the Polynomial Uniformizing a Given Compact Riemann Surface
%J Matematičeskie zametki
%D 2012
%P 597-607
%V 91
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a11/
%G ru
%F MZM_2012_91_4_a11
S. R. Nasyrov. Determination of the Polynomial Uniformizing a Given Compact Riemann Surface. Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 597-607. http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a11/

[1] T. Springer, Vvedenie v teoriyu rimanovykh poverkhnostei, IL, M., 1960 | MR | Zbl

[2] O. Forster, Rimanovy poverkhnosti, Mir, M., 1980 | MR | Zbl

[3] S. R. Nasyrov, Geometricheskie problemy teorii razvetvlennykh nakrytii rimanovykh poverkhnostei, Magarif, Kazan, 2008