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Mat. Zametki, 2012, Volume 91, Issue 4, Pages 597–607 (Mi mz8891)  

This article is cited in 5 scientific papers (total in 5 papers)

Determination of the Polynomial Uniformizing a Given Compact Riemann Surface

S. R. Nasyrov

Kazan (Volga Region) Federal University

Abstract: 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

DOI: https://doi.org/10.4213/mzm8891

Full text: PDF file (412 kB)
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English version:
Mathematical Notes, 2012, 91:4, 558–567

Bibliographic databases:

UDC: 517.54
Received: 14.09.2010

Citation: S. R. Nasyrov, “Determination of the Polynomial Uniformizing a Given Compact Riemann Surface”, Mat. Zametki, 91:4 (2012), 597–607; Math. Notes, 91:4 (2012), 558–567

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. N. Nakipov, S. R. Nasyrov, “Parametricheskii metod nakhozhdeniya aktsessornykh parametrov v obobschennykh integralakh Kristoffelya–Shvartsa”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 158, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2016, 202–220  mathnet  mathscinet  elib
    2. S. R. Nasyrov, “Uniformization of one-parametric families of complex tori”, Russian Math. (Iz. VUZ), 61:8 (2017), 36–45  mathnet  crossref  isi
    3. S. R. Nasyrov, “Uniformization of simply connected ramified coverings of the sphere by rational functions”, Dokl. Math., 96:2 (2017), 430–432  crossref  mathscinet  zmath  isi  scopus
    4. S. R. Nasyrov, “Uniformization of simply-connected ramified coverings of the sphere by rational functions”, Lobachevskii J. Math., 39:2, 3, SI (2018), 252–258  crossref  mathscinet  zmath  isi  scopus
    5. S. R. Nasyrov, “Families of elliptic functions and uniformization of complex tori with a unique point over infinity”, Probl. anal. Issues Anal., 7(25):2 (2018), 98–111  mathnet  crossref  elib
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