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Zero distribution of some difference polynomials
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作者 LI Qian LIU Dan HUANG Zhi-bo 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第3期392-402,共11页
In this paper,suppose that a,c∈C{0},c_(j)∈C(j=1,2,···,n) are not all zeros and n≥2,and f (z) is a finite order transcendental entire function with Borel finite exceptional value or with infinitely ma... In this paper,suppose that a,c∈C{0},c_(j)∈C(j=1,2,···,n) are not all zeros and n≥2,and f (z) is a finite order transcendental entire function with Borel finite exceptional value or with infinitely many multiple zeros,the zero distribution of difference polynomials of f (z+c)-af^(n)(z) and f (z)f (z+c_1)···f (z+c_n) are investigated.A number of examples are also presented to show that our results are best possible in a certain sense. 展开更多
关键词 difference polynomial zero distribution Borel exceptional value
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RITT-WU'S CHARACTERISTIC SET METHOD FOR ORDINARY DIFFERENCE POLYNOMIAL SYSTEMS WITH ARBITRARY ORDERING 被引量:6
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作者 高小山 袁春明 张桂林 《Acta Mathematica Scientia》 SCIE CSCD 2009年第4期1063-1080,共18页
In this paper, a Ritt-Wu's characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithm... In this paper, a Ritt-Wu's characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithms are also proposed. 展开更多
关键词 difference polynomial ascending chain characteristic set Ritt-Wu's zero decomposition theorem
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ON PROPERTIES OF DIFFERENCE POLYNOMIALS 被引量:6
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作者 陈宗煊 黄志波 郑秀敏 《Acta Mathematica Scientia》 SCIE CSCD 2011年第2期627-633,共7页
We study the value distribution of difference polynomials of meromorphic functions, and extend classical theorems of Tumura-Clunie type to difference polynomials. We also consider the value distribution of f(z)f(z ... We study the value distribution of difference polynomials of meromorphic functions, and extend classical theorems of Tumura-Clunie type to difference polynomials. We also consider the value distribution of f(z)f(z + c). 展开更多
关键词 difference polynomial Tumura-Clunie theorem value distribution.
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UNIQUENESS OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS
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作者 刘永 祁晓光 《Acta Mathematica Scientia》 SCIE CSCD 2014年第2期444-452,共9页
In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some exam... In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible. 展开更多
关键词 Meromorphic functions difference polynomials UNIQUENESS finite order
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Uniqueness of Entire Functions Related to Difference Polynomials
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作者 Pulak Sahoo 《Communications in Mathematics and Statistics》 SCIE 2015年第2期227-238,共12页
With the notion of weakly weighted sharing and relaxed weighted sharing,we investigate the uniqueness problems of certain type of difference polynomials sharing a small function.The results of the paper extend and gen... With the notion of weakly weighted sharing and relaxed weighted sharing,we investigate the uniqueness problems of certain type of difference polynomials sharing a small function.The results of the paper extend and generalize some recent results due to Meng(Math.Bohem.139:89-97,2014). 展开更多
关键词 UNIQUENESS Entire function difference polynomial
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ON ENTIRE SOLUTIONS OF SOME TYPE OF NONLINEAR DIFFERENCE EQUATIONS 被引量:2
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作者 Huifang LIU Zhiqiang MAO 《Acta Mathematica Scientia》 SCIE CSCD 2018年第3期819-828,共10页
In this article, the existence of finite order entire solutions of nonlinear difference equations fn+ Pd(z, f) = p1 eα1 z+ p2 eα2 z are studied, where n ≥ 2 is an integer, Pd(z, f) is a difference polynomial ... In this article, the existence of finite order entire solutions of nonlinear difference equations fn+ Pd(z, f) = p1 eα1 z+ p2 eα2 z are studied, where n ≥ 2 is an integer, Pd(z, f) is a difference polynomial in f of degree d(≤ n-2), p1, p2 are small meromorphic functions of ez, and α1, α2 are nonzero constants. Some necessary conditions are given to guarantee that the above equation has an entire solution of finite order. As its applications, we also find some type of nonlinear difference equations having no finite order entire solutions. 展开更多
关键词 Nevanlinna theory difference polynomial difference equation entire solution
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Meromorphic Functions Sharing One Value with Their Derivatives Concerning the Difference Operator
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作者 Sujoy Majumder 《Communications in Mathematics and Statistics》 SCIE 2017年第4期407-427,共21页
Let f(z)beanon-constantmeromorphicfunctionoffiniteorder,c∈C\{0}andk∈N.Suppose f(z)and f(k)(z+c)share1CM(IM),f(z)and f(z+c)share∞CM.If N(r,0;f)=S(r,f)(N(r,0;f(z))+N(r,0;f(k)(z+c))=S(r,f)),then either f(z)≡f(k)(z+c)... Let f(z)beanon-constantmeromorphicfunctionoffiniteorder,c∈C\{0}andk∈N.Suppose f(z)and f(k)(z+c)share1CM(IM),f(z)and f(z+c)share∞CM.If N(r,0;f)=S(r,f)(N(r,0;f(z))+N(r,0;f(k)(z+c))=S(r,f)),then either f(z)≡f(k)(z+c)or f(z)is a solution of the following equation:f((z+c)−1=a(z)(f(z)−1))f(z)+1 a(z)),and N(r,0;f(z)+1 a(z))=S(r,f)(f′(z+c)−1=a(z)(f(z)−1)(f(z)+1 a(z)))where a(z)(≡−1,0,∞)(a(z)(≡0,∞))is a meromorphic function satisfying T(r,a)=S(r,f).Also we exhibit some examples to show that the conditions of our results are the best possible. 展开更多
关键词 UNIQUENESS Meromorphic function·Shift operator difference polynomial Sharing values
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