{"title":"卡坦第二主定理的渐进相等性和一些概论","authors":"Y. Chen","doi":"10.1007/s10476-024-00043-8","DOIUrl":null,"url":null,"abstract":"<p>Motivated by [19] and [10], we define the modified proximity function <span>\\(\\overline{m}_{q}(f,r)\\)</span> for entire curves in complex projective space <span>\\(\\mathbf{P}^n\\mathbf{C}\\)</span>, and establish an asymptotic equality of Cartan's Second Main Theorem. This is a generalization of [19, Theorem 1.6] for transcendental meromorphic functions. Moreover, we strengthen the result to entire curves of finite order and holomorphic mappings over multiple variables.\n</p>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An asymptotic equality of Cartan's Second Main Theorem and some generalizations\",\"authors\":\"Y. Chen\",\"doi\":\"10.1007/s10476-024-00043-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Motivated by [19] and [10], we define the modified proximity function <span>\\\\(\\\\overline{m}_{q}(f,r)\\\\)</span> for entire curves in complex projective space <span>\\\\(\\\\mathbf{P}^n\\\\mathbf{C}\\\\)</span>, and establish an asymptotic equality of Cartan's Second Main Theorem. This is a generalization of [19, Theorem 1.6] for transcendental meromorphic functions. Moreover, we strengthen the result to entire curves of finite order and holomorphic mappings over multiple variables.\\n</p>\",\"PeriodicalId\":55518,\"journal\":{\"name\":\"Analysis Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10476-024-00043-8\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10476-024-00043-8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
An asymptotic equality of Cartan's Second Main Theorem and some generalizations
Motivated by [19] and [10], we define the modified proximity function \(\overline{m}_{q}(f,r)\) for entire curves in complex projective space \(\mathbf{P}^n\mathbf{C}\), and establish an asymptotic equality of Cartan's Second Main Theorem. This is a generalization of [19, Theorem 1.6] for transcendental meromorphic functions. Moreover, we strengthen the result to entire curves of finite order and holomorphic mappings over multiple variables.
期刊介绍：
Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx).
The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx).
The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.
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