scholarly journals On the singularities of the inverse to a meromorphic function of finite order

1995 ◽  
pp. 355-373 ◽  
Author(s):  
Walter Bergweiler ◽  
Alexandre Eremenko
Keyword(s):  
Meromorphic Function ◽  
Finite Order

scholarly journals On Properties of Differences Polynomials about Meromorphic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Jianming Qi ◽  
Jie Ding ◽  
Wenjun Yuan
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Special Class ◽  
Meromorphic Functions ◽  
Value Distribution ◽  
Class Difference ◽  
Difference Polynomial

We study the value distribution of a special class difference polynomial about finite order meromorphic function. Our methods of the proof are also different from ones in the previous results by Chen (2011), Liu and Laine (2010), and Liu and Yang (2009).

scholarly journals Value distribution of meromorphic functions concerning rational functions and differences

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mingliang Fang ◽  
Degui Yang ◽  
Dan Liu
Keyword(s):  
Positive Integer ◽  
Meromorphic Function ◽  
Rational Function ◽  
Finite Order ◽  
Meromorphic Functions ◽  
Rational Functions ◽  
Value Distribution ◽  
Exponent Of Convergence ◽  
Nonzero Constant ◽  
Zero Points

AbstractLet c be a nonzero constant and n a positive integer, let f be a transcendental meromorphic function of finite order, and let R be a nonconstant rational function. Under some conditions, we study the relationships between the exponent of convergence of zero points of $f-R$ f − R , its shift $f(z+nc)$ f ( z + n c ) and the differences $\Delta _{c}^{n} f$ Δ c n f .

scholarly journals Logarithmic derivative estimates of meromorphic functions of finite order in the half-plane

2020 ◽  
Vol 54 (2) ◽  
pp. 172-187
Author(s):  
I.E. Chyzhykov ◽  
A.Z. Mokhon'ko
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Half Plane ◽  
Meromorphic Functions ◽  
Logarithmic Derivative ◽  
Sharp Estimates ◽  
Exceptional Sets ◽  
Upper Half Plane ◽  
Logarithmic Derivatives

We established new sharp estimates outside exceptional sets for of the logarithmic derivatives $\frac{d^ {k} \log f(z)}{dz^k}$ and its generalization $\frac{f^{(k)}(z)}{f^{(j)}(z)}$, where $f$ is a meromorphic function $f$ in the upper half-plane, $k>j\ge0$ are integers. These estimates improve known estimates due to the second author in the class of meromorphic functions of finite order.Examples show that size of exceptional sets are best possible in some sense.

scholarly journals A note on a result of Singh and Kulkarni

2000 ◽  
Vol 23 (4) ◽  
pp. 285-288 ◽  
Author(s):  
Mingliang Fang
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Transcendental Meromorphic Function

We prove that iffis a transcendental meromorphic function of finite order and∑a≠∞δ(a,f)+δ(∞,f)=2, thenK(f(k))=2k(1−δ(∞,f))1+k−kδ(∞,f), whereK(f(k))=limr→∞N(r,1/f(k))+N(r,f(k))T(r,f(k))This result improves a result by Singh and Kulkarni.

scholarly journals Filling Disks of Hayman Type of Meromorphic Functions

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Nan Wu ◽  
Zuxing Xuan
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Meromorphic Functions

We obtain the existence of the filling disks with respect to Hayman directions. We prove that, under the conditionlimsupr→∞⁡(Tr,f/log⁡r3)=∞, there exists a sequence of filling disks of Hayman type, and these filling disks can determine a Hayman direction. Every meromorphic function of positive and finite orderρhas a sequence of filling disks of Hayman type, which can also determine a Hayman direction of orderρ.

scholarly journals Uniqueness of Functions with Its Shifts or Difference Operators

2018 ◽  
Author(s):  
Rajshree Dhar
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Difference Operator ◽  
Difference Operators

It is shown that if a non-constant meromorphic function f(z) is of finite order and shares certain values with its shifts/difference operators then f(z) coincides with that particular shift/difference operator.

scholarly journals On the Complex Oscillation of Meromorphic Solutions of Nonhomogeneous Linear Differential Equations with Meromorphic Coefficients

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Chuang-Xin Chen ◽  
Ning Cui ◽  
Zong-Xuan Chen
Keyword(s):  
Differential Equation ◽  
Meromorphic Function ◽  
Differential Equations ◽  
Rational Function ◽  
Finite Order ◽  
Order Differential Equation ◽  
Higher Order ◽  
Meromorphic Solutions ◽  
Complex Oscillation ◽  
Linear Differential

In this paper, we study the higher order differential equation f k + B f = H , where B is a rational function, having a pole at ∞ of order n > 0 , and H ≡ 0 is a meromorphic function with finite order, and obtain some properties related to the order and zeros of its meromorphic solutions.

scholarly journals On the common right factors of meromorphic functions

1997 ◽  
Vol 55 (3) ◽  
pp. 395-403 ◽  
Author(s):  
Tuen-Wai Ng ◽  
Chung-Chun Yang
Keyword(s):  
Entire Function ◽  
Meromorphic Function ◽  
Rational Function ◽  
Finite Order ◽  
Meromorphic Functions ◽  
Transcendental Meromorphic Function ◽  
The Common ◽  
Periodic Entire Function

In this paper, common right factors (in the sense of composition) of p1 + p2F and p3 + p4F are investigated. Here, F is a transcendental meromorphic function and pi's are non-zero polynomials. Moreover, we also prove that the quotient (p1 + p2F)/(p3 + p4F) is pseudo-prime under some restrictions on F and the pi's. As an application of our results, we have proved that R (z) H (z)is pseudo-prime for any nonconstant rational function R (z) and finite order periodic entire function H (z).

A note on Hayman’s conjecture

2020 ◽  
Vol 31 (06) ◽  
pp. 2050048
Author(s):  
Ta Thi Hoai An ◽  
Nguyen Viet Phuong
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Complex Plane ◽  
Function Theory ◽  
Differential Polynomials ◽  
Research Problems

In this paper, we will give suitable conditions on differential polynomials [Formula: see text] such that they take every finite nonzero value infinitely often, where [Formula: see text] is a meromorphic function in complex plane. These results are related to Problems 1.19 and 1.20 in a book of Hayman and Lingham [Research Problems in Function Theory, preprint (2018), https://arxiv.org/pdf/1809.07200.pdf ]. As consequences, we give a new proof of the Hayman conjecture. Moreover, our results allow differential polynomials [Formula: see text] to have some terms of any degree of [Formula: see text] and also the hypothesis [Formula: see text] in [Theorem 2 of W. Bergweiler and A. Eremenko, On the singularities of the inverse to a meromorphic function of finite order, Rev. Mat. Iberoamericana 11(2) (1995) 355–373] is replaced by [Formula: see text] in our result.

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