Annales Academię Scientiarum Fennicę
Mathematica
Volumen 38, 2013, 455-471
Changshu Institute of Technology, Department of Mathematics
Changshu, Jiangsu 215500, P.R. China; jmchang 'at' cslg.edu.cn
Chinese Academy of Sciences, AMSS, Institute of Mathematics
Beijing 100190, P.R. China; wangyf 'at' math.ac.cn
Abstract. We continue our previous study on the Bank-Laine type functions: meromorphic functions f that satisfy f(z) = 0 <=> f'(z) \in {a,b} on the plane, where a,b are two distinct nonzero values. Using quasi-normality, we prove that there is no transcendental meromorphic function with this property when the quotient a/b is a positive integer. Moreover, we prove a quasi-normal criterion for families of such functions. This completes our previous results.
2010 Mathematics Subject Classification: Primary 30D35, 30D45.
Key words: Meromorphic functions, Bank-Laine functions, quasi-normality, shared values and sets.
Reference to this article: J. Chang and Y. Wang: On Bank-Laine type functions. Ann. Acad. Sci. Fenn. Math. 38 (2013), 455-471.
doi:10.5186/aasfm.2013.3832
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