内万林纳理论通过全纯形式

IF 0.7 3区数学 Q2 MATHEMATICS

Pacific Journal of Mathematics Pub Date : 2022-01-07 DOI:10.2140/pjm.2022.319.55

Xianjing Dong, Shuangshuang Yang

{"title":"内万林纳理论通过全纯形式","authors":"Xianjing Dong, Shuangshuang Yang","doi":"10.2140/pjm.2022.319.55","DOIUrl":null,"url":null,"abstract":". This paper re-develops Nevanlinna theory for meromorphic functions on C in the viewpoint of holomorphic forms. According to our observation, Nevanlinna’s functions can be formulated by a holomorphic form. Applying this thought to Riemann surfaces, one then extends the deﬁnition of Nevanlinna’s functions using a holomorphic form S . With the new settings, an analogue of Nevanlinna theory on the S -exhausted Riemann surfaces is obtained, which is viewed as a generalization of the classical Nevanlinna theory for C and D .","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Nevanlinna theory via holomorphic forms\",\"authors\":\"Xianjing Dong, Shuangshuang Yang\",\"doi\":\"10.2140/pjm.2022.319.55\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". This paper re-develops Nevanlinna theory for meromorphic functions on C in the viewpoint of holomorphic forms. According to our observation, Nevanlinna’s functions can be formulated by a holomorphic form. Applying this thought to Riemann surfaces, one then extends the deﬁnition of Nevanlinna’s functions using a holomorphic form S . With the new settings, an analogue of Nevanlinna theory on the S -exhausted Riemann surfaces is obtained, which is viewed as a generalization of the classical Nevanlinna theory for C and D .\",\"PeriodicalId\":54651,\"journal\":{\"name\":\"Pacific Journal of Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-01-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pacific Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2140/pjm.2022.319.55\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pacific Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/pjm.2022.319.55","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

摘要

。本文从全纯形式的角度重新发展了C上亚纯函数的Nevanlinna理论。根据我们的观察，内万林纳函数可以用全纯形式表示。将这一思想应用于黎曼曲面，然后用全纯形式S扩展了内万林纳函数的定义。在新的条件下，得到了S -耗尽黎曼曲面上Nevanlinna理论的类比，这被视为经典Nevanlinna理论在C和D上的推广。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Nevanlinna theory via holomorphic forms

. This paper re-develops Nevanlinna theory for meromorphic functions on C in the viewpoint of holomorphic forms. According to our observation, Nevanlinna’s functions can be formulated by a holomorphic form. Applying this thought to Riemann surfaces, one then extends the deﬁnition of Nevanlinna’s functions using a holomorphic form S . With the new settings, an analogue of Nevanlinna theory on the S -exhausted Riemann surfaces is obtained, which is viewed as a generalization of the classical Nevanlinna theory for C and D .

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Pacific Journal of Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Founded in 1951, PJM has published mathematics research for more than 60 years. PJM is run by mathematicians from the Pacific Rim. PJM aims to publish high-quality articles in all branches of mathematics, at low cost to libraries and individuals. The Pacific Journal of Mathematics is incorporated as a 501(c)(3) California nonprofit.