Geodesic
Uniformization of one-parametric families of complex tori
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2017), pp. 42-52

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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. 
@article{IVM_2017_8_a3,
     author = {S. R. Nasyrov},
     title = {Uniformization of one-parametric families of complex tori},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {42--52},
     publisher = {mathdoc},
     number = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_8_a3/}
}
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S. R. Nasyrov. Uniformization of one-parametric families of complex tori. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2017), pp. 42-52. http://geodesic.mathdoc.fr/item/IVM_2017_8_a3/