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Probl. Anal. Issues Anal., 2018, Volume 7(25), Issue 2, Pages 98–111 (Mi pa250)  

Families of elliptic functions and uniformization of complex tori with a unique point over infinity

S. R. Nasyrov

Kazan Federal University, 35 Kremlevskaya str., Kazan 420008, Russia

Abstract: We investigate the problem of describing a one-parametric family of elliptic functions which uniformizes a given family of ramified coverings of the Riemann sphere with maximal possible ramification over infinity. We find a PDE for the family of functions and use it to deduce a system of ODEs for their critical points.

Keywords: Riemann surface, complex torus, elliptic function, uniformization.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-41-160003
This work was supported by the Russian Foundation for Basic Research, grant 18-41-160003.


DOI: https://doi.org/10.15393/j3.art.2018.5290

Full text: PDF file (446 kB)
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Bibliographic databases:

UDC: 517.545
MSC: 30F10, 32G15
Received: 30.08.2018
Revised: 26.11.2018
Accepted:29.11.2018
Language:

Citation: 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

Citation in format AMSBIB
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\paper Families of elliptic functions and uniformization of complex tori with a unique point over infinity
\jour Probl. Anal. Issues Anal.
\yr 2018
\vol 7(25)
\issue 2
\pages 98--111
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