{"title":"椭圆函数族与无穷上有唯一点的复环面均匀化","authors":"S. Nasyrov","doi":"10.15393/J3.ART.2018.5290","DOIUrl":null,"url":null,"abstract":". We investigate the problem of describing a one-para-metric 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.","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"6 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Families of elliptic functions and uniformization of complex tori with a unique point over infinity\",\"authors\":\"S. Nasyrov\",\"doi\":\"10.15393/J3.ART.2018.5290\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We investigate the problem of describing a one-para-metric 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.\",\"PeriodicalId\":41813,\"journal\":{\"name\":\"Problemy Analiza-Issues of Analysis\",\"volume\":\"6 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2018-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Problemy Analiza-Issues of Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15393/J3.ART.2018.5290\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Problemy Analiza-Issues of Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15393/J3.ART.2018.5290","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Families of elliptic functions and uniformization of complex tori with a unique point over infinity
. We investigate the problem of describing a one-para-metric 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.
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