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Estimates for the zeros of differences of meromorphic functions
Chen, ZongXuan,Shon, Kwang Ho Springer-Verlag 2009 Science in China. Series A, Mathematics Vol.52 No.11
<P>Let f be a transcendental meromorphic function and g(z) = f (z + c(1)) + f(z + c(2)) - 2f(z) and g(2) (z) = f (z + c(1)) . f (z + c(2)) - f(2)(z). The exponents of convergence of zeros of differences g(z), g(2)(z), g(z)/f(z), and g(2)(z)/f(2)(z) are estimated accurately.</P>
MEROMORPHIC SOLUTIONS OF SOME q-DIFFERENCE EQUATIONS
Chen, Baoqin,Chen, Zongxuan Korean Mathematical Society 2011 대한수학회보 Vol.48 No.6
We consider meromorphic solutions of q-difference equations of the form $$\sum_{j=o}^{n}a_j(z)f(q^jz)=a_{n+1}(z),$$ where $a_0(z)$, ${\ldots}$, $a_{n+1}(z)$ are meromorphic functions, $a_0(z)a_n(z)$ ≢ 0 and $q{\in}\mathbb{C}$ such that 0 < |q| ${\leq}$ 1. We give a new estimate on the upper bound for the length of the gap in the power series of entire solutions for the case 0 < |q| < 1 and n = 2. Some growth estimates for meromorphic solutions are also given in the cases 0 < |q| < 1. Moreover, we investigate zeros and poles of meromorphic solutions for the case |q| = 1.
Meromorphic solutions of some q-difference equations
BaoQin Chen,ZongXuan Chen 대한수학회 2011 대한수학회보 Vol.48 No.6
We consider meromorphic solutions of $q$-difference equations of the form [수식]=a_(n+1)(z), where a_0(z), ...,a_(n+1)(z) are meromorphic functions, a_0(z)a_n(z)[기호] 0 and q∈C such that 0<|q|≤ 1. We give a new estimate on the upper bound for the length of the gap in the power series of entire solutions for the case 0<|q|<1 and n=2. Some growth estimates for meromorphic solutions are also given in the cases 0<|q|<1 and |q|=1. Moreover, we investigate zeros and poles of meromorphic solutions for the case |q|=1.
THE ZEROS DISTRIBUTION OF SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS IN AN ANGULAR DOMAIN
Huang, Zhibo,Chen, Zongxuan Korean Mathematical Society 2010 대한수학회보 Vol.47 No.3
In this paper, we investigate the zeros distribution and Borel direction for the solutions of linear homogeneous differential equation $f^{(n)}+A_{n-2}(z)f^{(n-2)}+{\cdots}+A_1(z)f'+A_0(z)f=0(n{\geq}2)$ in an angular domain. Especially, we establish a relation between a cluster ray of zeros and Borel direction.
THE ZEROS DISTRIBUTION OF SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS IN AN ANGULAR DOMAIN
Zhibo Huang,Zongxuan Chen 대한수학회 2010 대한수학회보 Vol.47 No.3
In this paper, we investigate the zeros distribution and Borel direction for the solutions of linear homogeneous differential equation f(n) + An−2(z)f(n−2) + · · · + A1(z)f' + A0(z)f = 0 (n ≥ 2)in an angular domain. Especially, we establish a relation between a cluster ray of zeros and Borel direction.