On the singularities of the inverse to a meromorphic function on finite order
- Autores: Alexandre Eremenko, Walter Bergweiler
- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 11, Nº 2, 1995, págs. 355-374
- Idioma: inglés
- DOI: 10.4171/rmi/176
- Títulos paralelos:
- Singularidades de la inversa de una función meromórfica de orden finito.
- Enlaces
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Resumen
Our main result implies the following theorem: Let f be a transcendental meromorphic function in the complex plane. If f has finite order ?, then every asymptotic value of f, except at most 2? 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. The proof makes use of the iteration theory of meromorphic functions
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