Two Entire Functions Sharing One Small Function CM and Two Other Small Functions IM
Copyright policy )Two Entire Functions Sharing One Small Function CM and Two Other Small Functions IM
The author proves the following result: Let \(f\) and \(g\) be two nonconstant entire functions. Let \(a_1\), \(a_2\) and \(a_3\) be three distinct small meromorphic functions with respect to \(f\) and \(g\). If \(f\) and \(g\) share \(a_1\), \(a_2\) IM and share \(a_3\) CM, then \[ f=\frac{\alpha_1 g+ \beta_1}{\alpha_2 g +\beta_2}, \] where \(\alpha_i\), \(\beta_i\), \(i=1,2\), are small meromorphic functions with respect to \(f\) and \(g\). Here CM (resp., IM) is the abbreviation of counting multiplicity (resp., ignoring multiplicity). A more general result was obtained by \textit{P. Li} [J. Math. Anal. Appl. 263, 316-326 (2001; Zbl 1007.30020)].
- Department of Mathematics
- Wuhan University
- Wuhan University
- Shandong Women’s University China (People's Republic of)
- Wuhan University China (People's Republic of)
Entire functions of one complex variable (general theory), Applied Mathematics, entire function, meromorphic function, sharing value, small function, value distribution, quasi-Möbius transformation, Analysis, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
Entire functions of one complex variable (general theory), Applied Mathematics, entire function, meromorphic function, sharing value, small function, value distribution, quasi-Möbius transformation, Analysis, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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