Uniqueness Theorem of Algebroidal Functions in an Angular Domain
Received:March 29, 2008  Revised:January 05, 2009
Key Words: algebroidal function   order   uniqueness.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10471048) and the Research Fund of the Doctoral Program of Higher Education (Grant No.20050574002).
Author NameAffiliation
Hui Fang LIU Institute of Mathematics and Informatics, Jiangxi Normal University, Jiangxi 330027, P. R. China
School of Mathematics, South China Normal University, Guangdong 510631, P. R. China 
Dao Chun SUN School of Mathematics, South China Normal University, Guangdong 510631, P. R. China 
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Abstract:
      Let $W(z)$ and $M(z)$ be $v$-valued and $k$-valued algebroidal functions respectively, $\triangle(\theta)$ be a $b$-cluster line of order $\infty$ (or $\rho(r)$) of $W(z)$ (or $M(z)$). It is shown that $W(z)\equiv M(z)$ provided $\overline{E}(a_j,W(z))=\overline{E}(a_j,M(z))~(j=1,\ldots,2v 2k 1)$ holds in the angular domain $\Omega(\theta-\delta,\theta \delta)$, where $b,a_j~(j=1,\ldots,2v 2k 1)$ are complex constants. The same results are obtained for the case that $\triangle(\theta)$ is a Borel direction of order $\infty$ (or $\rho(r)$) of $W(z)$ (or $M(z)$).
Citation:
DOI:10.3770/j.issn:1000-341X.2010.03.016
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