{"title":"Two results on the value distribution of meromorphic functions","authors":"Degui Yang, Zhiying He, Dan Liu","doi":"10.1515/math-2024-0004","DOIUrl":null,"url":null,"abstract":"In this article, we prove two results on the value distribution of meromorphic functions. Using the theorem of Yamanoi, the first result gives a precise estimation of the relationship between the characteristic function of a meromorphic function and its <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0004_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>k</m:mi> </m:math> <jats:tex-math>k</jats:tex-math> </jats:alternatives> </jats:inline-formula>th derivative in a concise form. This result extends and improves some results of Shan, Singh, Gopalakrishna, Edrei, Weitsman, Yang, Wu and Wu, etc. The second result answers a conjecture posed by C. C. Yang. This conjecture turned to be false by a counter-example, but it will be true with an additional condition.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"55 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Open Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/math-2024-0004","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we prove two results on the value distribution of meromorphic functions. Using the theorem of Yamanoi, the first result gives a precise estimation of the relationship between the characteristic function of a meromorphic function and its kkth derivative in a concise form. This result extends and improves some results of Shan, Singh, Gopalakrishna, Edrei, Weitsman, Yang, Wu and Wu, etc. The second result answers a conjecture posed by C. C. Yang. This conjecture turned to be false by a counter-example, but it will be true with an additional condition.
在这篇文章中，我们证明了两个关于分形函数值分布的结果。利用 Yamanoi 定理，第一个结果以简洁的形式给出了分形函数特征函数与其 k k th 导数之间关系的精确估计。这一结果扩展并改进了 Shan、Singh、Gopalakrishna、Edrei、Weitsman、Yang、Wu 和 Wu 等人的一些结果。第二个结果回答了 C. C. Yang 提出的一个猜想。通过一个反例，这个猜想变成了假的，但只要附加一个条件，它就会变成真的。
期刊介绍：
Open Mathematics - formerly Central European Journal of Mathematics
Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication.
Open Mathematics is listed in Thomson Reuters - Current Contents/Physical, Chemical and Earth Sciences. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind.
Aims and Scope
The journal aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes:
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