Our main result implies the following theorem: Let be a transcendental meromorphic function in the complex plane. If has finite order , then every asymptotic value of , except at most of them, is a limit point of critical values of .
We give several applications of this theorem. For example we prove that if is a transcendental meromorphic function then with takes every finite non-zero value infinitely often. This proves a conjecture of Hayman. The proof makes use of the iteration theory of meromorphic functions.
Cite this article
Walter Bergweiler, Alexandre Eremenko, On the singularities of the inverse to a meromorphic function of finite order. Rev. Mat. Iberoam. 11 (1995), no. 2, pp. 355–373