{"title":"超几何函数值的算术性质","authors":"P. Ivankov","doi":"10.1070/SM1992V072N01ABEH001413","DOIUrl":null,"url":null,"abstract":"The author proposes an effective method of constructing a linear approximating form for a hypergeometric function of general type and its derivatives, which has a zero of the maximal possible order at z = 0. This construction is applied to the study of arithmetic properties of values of these functions at points of an imaginary quadratic field.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"18 2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":"{\"title\":\"ON ARITHMETIC PROPERTIES OF THE VALUES OF HYPERGEOMETRIC FUNCTIONS\",\"authors\":\"P. Ivankov\",\"doi\":\"10.1070/SM1992V072N01ABEH001413\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The author proposes an effective method of constructing a linear approximating form for a hypergeometric function of general type and its derivatives, which has a zero of the maximal possible order at z = 0. This construction is applied to the study of arithmetic properties of values of these functions at points of an imaginary quadratic field.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"18 2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"16\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1992V072N01ABEH001413\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1992V072N01ABEH001413","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ON ARITHMETIC PROPERTIES OF THE VALUES OF HYPERGEOMETRIC FUNCTIONS
The author proposes an effective method of constructing a linear approximating form for a hypergeometric function of general type and its derivatives, which has a zero of the maximal possible order at z = 0. This construction is applied to the study of arithmetic properties of values of these functions at points of an imaginary quadratic field.
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