On the value distribution of differential polynomials of meromorphic functions

Yan Xu, and Huiling Qiu. "On the value distribution of differential polynomials of meromorphic functions." Annales Polonici Mathematici 98.3 (2010): 283-289. <http://eudml.org/doc/280282>.

@article{YanXu2010,
abstract = {Let f be a transcendental meromorphic function of infinite order on ℂ, let k ∈ ℕ and $φ = Re^P$, where R ≢ 0 is a rational function and P is a polynomial, and let $a₀, a₁,...,a_\{k-1\}$ be holomorphic functions on ℂ. If all zeros of f have multiplicity at least k except possibly finitely many, and $f = 0 ⇔ f^\{(k)\} + a_\{k-1\}f^\{(k-1)\} + ⋯ + a₀f = 0$, then $f^\{(k)\} + a_\{k-1\}f^\{(k-1)\} + ⋯ + a₀f - φ$ has infinitely many zeros.},
author = {Yan Xu, Huiling Qiu},
journal = {Annales Polonici Mathematici},
keywords = {value distribution; differential polynomials of meromorphic functions; transcendental meromorphic function of infinite order},
language = {eng},
number = {3},
pages = {283-289},
title = {On the value distribution of differential polynomials of meromorphic functions},
url = {http://eudml.org/doc/280282},
volume = {98},
year = {2010},
}

TY - JOUR
AU - Yan Xu
AU - Huiling Qiu
TI - On the value distribution of differential polynomials of meromorphic functions
JO - Annales Polonici Mathematici
PY - 2010
VL - 98
IS - 3
SP - 283
EP - 289
AB - Let f be a transcendental meromorphic function of infinite order on ℂ, let k ∈ ℕ and $φ = Re^P$, where R ≢ 0 is a rational function and P is a polynomial, and let $a₀, a₁,...,a_{k-1}$ be holomorphic functions on ℂ. If all zeros of f have multiplicity at least k except possibly finitely many, and $f = 0 ⇔ f^{(k)} + a_{k-1}f^{(k-1)} + ⋯ + a₀f = 0$, then $f^{(k)} + a_{k-1}f^{(k-1)} + ⋯ + a₀f - φ$ has infinitely many zeros.
LA - eng
KW - value distribution; differential polynomials of meromorphic functions; transcendental meromorphic function of infinite order
UR - http://eudml.org/doc/280282
ER -