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

Walter Bergweiler; Alexander Eremenko

Revista Matemática Iberoamericana (1995)

- Volume: 11, Issue: 2, page 355-373
- ISSN: 0213-2230

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topBergweiler, Walter, and Eremenko, Alexander. "On the singularities of the inverse to a meromorphic function of finite order.." Revista Matemática Iberoamericana 11.2 (1995): 355-373. <http://eudml.org/doc/39474>.

@article{Bergweiler1995,

abstract = {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. The proof makes use of the iteration theory of meromorphic functions.},

author = {Bergweiler, Walter, Eremenko, Alexander},

journal = {Revista Matemática Iberoamericana},

keywords = {Función meromorfa; Superficies Riemann; Ley límite; Teoría de singularidades},

language = {eng},

number = {2},

pages = {355-373},

title = {On the singularities of the inverse to a meromorphic function of finite order.},

url = {http://eudml.org/doc/39474},

volume = {11},

year = {1995},

}

TY - JOUR

AU - Bergweiler, Walter

AU - Eremenko, Alexander

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

JO - Revista Matemática Iberoamericana

PY - 1995

VL - 11

IS - 2

SP - 355

EP - 373

AB - 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. The proof makes use of the iteration theory of meromorphic functions.

LA - eng

KW - Función meromorfa; Superficies Riemann; Ley límite; Teoría de singularidades

UR - http://eudml.org/doc/39474

ER -

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