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

Walter BergweilerAlexander Eremenko — 1995

Revista Matemática Iberoamericana

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 of Hayman....

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