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Izv. Vyssh. Uchebn. Zaved. Mat., 2017, Number 8, Pages 42–52
(Mi ivm9267)
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This article is cited in 1 scientific paper (total in 1 paper)
Uniformization of one-parametric families of complex tori
S. R. Nasyrov Kazan Federal University,
18 Kremlyovskaya str., Kazan, 420008 Russia
Abstract:
We suggest an approximate method to find an elliptic function uniformizing compact Riemann surface of genus 1 which is given as a ramified covering of the Riemann sphere. The method is based on including the surface into a smooth one-parametric family. We deduce a system of ordinary differential equations for critical points of elliptic functions uniformizing surfaces of the family.
Keywords:
Riemann surface, complex torus, ramified covering, elliptic function, uniformization, one-parametric families of meromorphic functions.
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:8, 36–45
Bibliographic databases:
UDC:
517.5 Received: 07.04.2016
Citation:
S. R. Nasyrov, “Uniformization of one-parametric families of complex tori”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 8, 42–52; Russian Math. (Iz. VUZ), 61:8 (2017), 36–45
Citation in format AMSBIB
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\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2017
\issue 8
\pages 42--52
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\jour Russian Math. (Iz. VUZ)
\yr 2017
\vol 61
\issue 8
\pages 36--45
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http://mi.mathnet.ru/eng/ivm9267 http://mi.mathnet.ru/eng/ivm/y2017/i8/p42
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This publication is cited in the following articles:
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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
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