{"title":"Value distribution of a pair of meromorphic functions","authors":"","doi":"10.1016/j.jmaa.2024.128914","DOIUrl":null,"url":null,"abstract":"<div><div>The well-known Picard theorem shows only what happens on the Picard exceptional value of a meromorphic function <em>f</em>. In this paper, we mainly consider what happens on the common or different Picard exceptional values of two or three meromorphic functions with certain types. For instance, we will provide some new results and discussions for the generalized Picard exceptional values or small functions of a pair of meromorphic functions <span><math><msup><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msup><msup><mrow><mi>g</mi></mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math></span> and <span><math><msup><mrow><mi>g</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>f</mi></mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math></span>, these two functions are the crossed variants of the complex differential polynomials in Hayman's conjecture, where <em>n</em>, <em>m</em> are positive integers and <span><math><mi>k</mi><mo>≥</mo><mn>0</mn></math></span>. We give more details on the case that <span><math><mi>f</mi><msup><mrow><mi>g</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> and <span><math><mi>g</mi><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> when <em>f</em> and <em>g</em> are exponential polynomials in particular.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24008369","RegionNum":3,"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
The well-known Picard theorem shows only what happens on the Picard exceptional value of a meromorphic function f. In this paper, we mainly consider what happens on the common or different Picard exceptional values of two or three meromorphic functions with certain types. For instance, we will provide some new results and discussions for the generalized Picard exceptional values or small functions of a pair of meromorphic functions and , these two functions are the crossed variants of the complex differential polynomials in Hayman's conjecture, where n, m are positive integers and . We give more details on the case that and when f and g are exponential polynomials in particular.
期刊介绍:
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
Papers are sought which employ one or more of the following areas of classical analysis:
• Analytic number theory
• Functional analysis and operator theory
• Real and harmonic analysis
• Complex analysis
• Numerical analysis
• Applied mathematics
• Partial differential equations
• Dynamical systems
• Control and Optimization
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