{"title":"函数的黎曼曲面及其分数积分","authors":"W. Fabian","doi":"10.1017/S0950184300003116","DOIUrl":null,"url":null,"abstract":"2. Transformation of Riemann surfaces. Theorem 1. Let f(z) be analytic within a circle with centre at a, and which contains I in its interior. Then a is a branch-point of D~ (la)f(z) for non-integral values of X. If A is a rational fraction rjg expressed in its lowest terms, then a is the vertex of a cycle of s roots. If A is irrational or complex, then a is the vertex of an infinite number of roots.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Riemann surfaces of a function and its fractional integral\",\"authors\":\"W. Fabian\",\"doi\":\"10.1017/S0950184300003116\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"2. Transformation of Riemann surfaces. Theorem 1. Let f(z) be analytic within a circle with centre at a, and which contains I in its interior. Then a is a branch-point of D~ (la)f(z) for non-integral values of X. If A is a rational fraction rjg expressed in its lowest terms, then a is the vertex of a cycle of s roots. If A is irrational or complex, then a is the vertex of an infinite number of roots.\",\"PeriodicalId\":417997,\"journal\":{\"name\":\"Edinburgh Mathematical Notes\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Edinburgh Mathematical Notes\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/S0950184300003116\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Edinburgh Mathematical Notes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/S0950184300003116","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Riemann surfaces of a function and its fractional integral
2. Transformation of Riemann surfaces. Theorem 1. Let f(z) be analytic within a circle with centre at a, and which contains I in its interior. Then a is a branch-point of D~ (la)f(z) for non-integral values of X. If A is a rational fraction rjg expressed in its lowest terms, then a is the vertex of a cycle of s roots. If A is irrational or complex, then a is the vertex of an infinite number of roots.
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