{"title":"亚纯函数族的正规准则和共享值的进一步结果","authors":"Jianm ng Qi","doi":"10.7153/JCA-2019-14-06","DOIUrl":null,"url":null,"abstract":". Let k be a positive integer and let F be a family of meromorphic functions in the domain D all of whose zeros with multiplicity at least k . Let P be a polynomial and P have at least one simple zero, p = deg ( P ) (cid:2) k + 2. If, for each pair f , g ∈ F , P ( f ) G m ( f ) and P ( g ) G m ( g ) share a nonzero constant b ignoring multiplicity in D, where G ( f ) = P ( f ( k ) )+ H ( f ) is a differential polynomial of f satisfying w deg | H (cid:3) kmql + mq + 1 or w ( H ) − deg ( H ) < qk , and q > l (cid:2) k + 1 is a positive integer, then F is normal in D.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Further results about normal criteria and shared values for families of meromorphic functions\",\"authors\":\"Jianm ng Qi\",\"doi\":\"10.7153/JCA-2019-14-06\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Let k be a positive integer and let F be a family of meromorphic functions in the domain D all of whose zeros with multiplicity at least k . Let P be a polynomial and P have at least one simple zero, p = deg ( P ) (cid:2) k + 2. If, for each pair f , g ∈ F , P ( f ) G m ( f ) and P ( g ) G m ( g ) share a nonzero constant b ignoring multiplicity in D, where G ( f ) = P ( f ( k ) )+ H ( f ) is a differential polynomial of f satisfying w deg | H (cid:3) kmql + mq + 1 or w ( H ) − deg ( H ) < qk , and q > l (cid:2) k + 1 is a positive integer, then F is normal in D.\",\"PeriodicalId\":73656,\"journal\":{\"name\":\"Journal of classical analysis\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of classical analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/JCA-2019-14-06\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of classical analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/JCA-2019-14-06","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
。设k是一个正整数，设F是D域中的一组亚纯函数它们的0的多重性至少为k。设P是一个多项式，且P至少有一个简单零，P = deg (P) (cid:2) k + 2。如果每一对f, g∈f P (f) g m (f)和P (g) g m (g)共享一个非零常数b D忽视多样性,在g (f) = P (f (k)) + H f (f)是一个微分多项式满足w度| H (cid: 3) kmql + mq + 1或w (H)−度(H) < qk, q > l (cid: 2) k + 1是一个正整数,然后在D f是正常的。
Further results about normal criteria and shared values for families of meromorphic functions
. Let k be a positive integer and let F be a family of meromorphic functions in the domain D all of whose zeros with multiplicity at least k . Let P be a polynomial and P have at least one simple zero, p = deg ( P ) (cid:2) k + 2. If, for each pair f , g ∈ F , P ( f ) G m ( f ) and P ( g ) G m ( g ) share a nonzero constant b ignoring multiplicity in D, where G ( f ) = P ( f ( k ) )+ H ( f ) is a differential polynomial of f satisfying w deg | H (cid:3) kmql + mq + 1 or w ( H ) − deg ( H ) < qk , and q > l (cid:2) k + 1 is a positive integer, then F is normal in D.
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