Displaying similar documents to “Schwarzian derivatives of topologically finite meromorphic functions.”

On unique range sets of meromorphic functions in ℂ m

Xiao-Tian Bai, Qi Han (2007)

Archivum Mathematicum

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

Meromorphic extension spaces

Le Mau Hai, Nguyen Van Khue (1992)

Annales de l'institut Fourier

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The aim of the present paper is to study meromorphic extension spaces. The obtained results allow us to get the invariance of meromorphic extendibility under finite proper surjective holomorphic maps.

On the singularities of the inverse to a meromorphic function of finite order.

Walter Bergweiler, Alexander Eremenko (1995)

Revista Matemática Iberoamericana

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Our main result implies the following theorem: Let f be a transcendental meromorphic function in the complex plane. If f has finite order ρ, then every asymptotic value of f, except at most 2ρ of them, is a limit point of critical values of f. We give several applications of this theorem. For example we prove that if f is a transcendental meromorphic function then f'fn with n ≥ 1 takes every finite non-zero value infinitely often. This proves a conjecture...