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

S. R. Nasyrov
2018 Problemy Analiza  
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.
doi:10.15393/j3.art.2018.5290 fatcat:56nezkoexvhu5pv7qbqmwadqua