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On unique range sets of meromorphic functions in m

Xiao-Tian BaiQi Han — 2007

Archivum Mathematicum

By considering a question proposed by F. Gross concerning unique range sets of entire functions in , we study the unicity of meromorphic functions in m that share three distinct finite sets CM and obtain some results which reduce 5 c 3 ( ( m ) ) 9 to 5 c 3 ( ( m ) ) 6 .

On unicity of meromorphic functions due to a result of Yang - Hua

Xiao-Tian BaiQi Han — 2007

Archivum Mathematicum

This paper studies the unicity of meromorphic(resp. entire) functions of the form f n f ' and obtains the following main result: Let f and g be two non-constant meromorphic (resp. entire) functions, and let a { 0 } be a non-zero finite value. Then, the condition that E 3 ) ( a , f n f ' ) = E 3 ) ( a , g n g ' ) implies that either f = d g for some ( n + 1 ) -th root of unity d , or f = c 1 e c z and g = c 2 e - c z for three non-zero constants c , c 1 and c 2 with ( c 1 c 2 ) n + 1 c 2 = - a 2 provided that n 11 (resp. n 6 ). It improves a result of C. C. Yang and X. H. Hua. Also, some other related problems are discussed.

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