{"title":"具有四分之一整数参数的Appell第二超几何系统的Schwarz映射","authors":"Keiji Matsumoto, Shohei Osafune, T. Terasoma","doi":"10.2748/tmj.20201207","DOIUrl":null,"url":null,"abstract":"We study Schwarz's map for Appell's second system $\\cF_2$ of hypergeometric differential equations in two variables with parameters $a=c_1=c_2=\\frac{1}{2}$, $b_1=b_2=\\frac{1}{4}$. By using theta functions with characteristics, we give a defining equation of an analytic set in $\\C^2\\times \\H$ of its image, and express its inverse.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2019-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Schwarz's map for Appell's second hypergeometric system with quarter integer parameters\",\"authors\":\"Keiji Matsumoto, Shohei Osafune, T. Terasoma\",\"doi\":\"10.2748/tmj.20201207\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study Schwarz's map for Appell's second system $\\\\cF_2$ of hypergeometric differential equations in two variables with parameters $a=c_1=c_2=\\\\frac{1}{2}$, $b_1=b_2=\\\\frac{1}{4}$. By using theta functions with characteristics, we give a defining equation of an analytic set in $\\\\C^2\\\\times \\\\H$ of its image, and express its inverse.\",\"PeriodicalId\":54427,\"journal\":{\"name\":\"Tohoku Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2019-12-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tohoku Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2748/tmj.20201207\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tohoku Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2748/tmj.20201207","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Schwarz's map for Appell's second hypergeometric system with quarter integer parameters
We study Schwarz's map for Appell's second system $\cF_2$ of hypergeometric differential equations in two variables with parameters $a=c_1=c_2=\frac{1}{2}$, $b_1=b_2=\frac{1}{4}$. By using theta functions with characteristics, we give a defining equation of an analytic set in $\C^2\times \H$ of its image, and express its inverse.
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